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Last modification:
April 10, 2024
 
Patrick Winkert
patrick_winkert Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 1-0
MA 669
Straße des 17. Juni 136
10623 Berlin, Germany
+49 - 30 - 314 - 2 74 87
winkert(at)math.tu-berlin.de
Website at TU Berlin
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Patrick Winkert
Curriculum Vitae
Education
  • 2015: Habilitation in Mathematics (postdoctoral qualification, Dr.rer.nat.habil.), Thesis: Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Technische Universität Berlin, Berlin, Germany
  • 2009: Ph.D. in Mathematics (Dr.rer.nat.), Thesis: Comparison principles and multiple solutions for nonlinear elliptic problems, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany,
  • 2006: Master in Mathematics (Diploma in Mathematics), Thesis: T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Employment
  • since 2019: Research Assistant (permanent), Technische Universität Berlin, Berlin, Germany
  • since 2016: Privatdozent, Technische Universität Berlin, Berlin, Germany
  • Fall 2017: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2017: Guest Professor 'Applied Analysis', Humboldt-Universität zu Berlin, Berlin, Germany
  • Fall 2016: Substitute Professor 'Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • Spring 2016: Substitute Professor 'Applied Analysis', Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
  • 2009 – 2019: Research Assistant, Technische Universität Berlin, Berlin, Germany
  • 2006 – 2009: Research Assistant, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Patrick Winkert
Publications
Monographs
  1. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, Second Revised Edition, De Gruyter, Berlin, to appear 2024, ≈ x+700 pp.
    De Gruyter
  2. N.S. Papageorgiou, P. Winkert, Applied Nonlinear Functional Analysis. An Introduction, De Gruyter, Berlin, 2018, x+612 pp.
    De Gruyter
Editorials
  1. P. Candito, R. Livrea, P. Winkert, Special issue on the occasion of the 70th birthday of Professor Siegfried Carl, Nonlinear Anal. Real World Appl. 74 (2023), Paper No. 103959. Preprint   Journal   
Refereed Articles
  1. M.M. Frisch, P. Winkert, Boundedness, existence and uniqueness results for coupled gradient dependent elliptic systems with nonlinear boundary condition, Adv. Nonlinear Anal., accepted 2024. Preprint   Journal   
  2. F. Borer, S. Carl, P. Winkert, Elliptic p-Laplacian systems with nonlinear boundary condition, J. Math. Anal. Appl., accepted 2024. Preprint   Journal   arXiv
  3. E. Amoroso, G. Bonanno, G. D'Aguì, P. Winkert, Two solutions for Dirichlet double phase problems with variable exponents, Adv. Nonlinear Stud., accepted 2024. Preprint   Journal   
  4. H. Tao, L. Li, P. Winkert, Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in RN, Forum Math., accepted 2024. Preprint   Journal   
  5. N.S. Papageorgiou, F. Vetro, P. Winkert, Sequences of nodal solutions for critical double phase problems with variable exponents, Z. Angew. Math. Phys., accepted 2024. Preprint   Journal   
  6. W. Liu, G. Dai, P. Winkert, Multiple sign-changing solutions for superlinear (p,q)-equations in symmetrical expanding domains, Bull. Sci. Math. 191 (2024), Paper No. 103393, 21 pp. Preprint   Journal   
  7. E. Amoroso, A. Sciammetta, P. Winkert, Anisotropic (p⃗,q⃗)-Laplacian problems with superlinear nonlinearities, Commun. Anal. Mech. 16 (2024), no. 1, 1–23. Preprint   Journal   
  8. S. Zeng, V.D. Rădulescu, P. Winkert, Nonlocal double phase implicit obstacle problems with multivalued boundary conditions, SIAM J. Math. Anal. 56 (2024), no. 1, 877–912. Preprint   Journal   
  9. Á. Crespo-Blanco, P. Winkert, Nehari manifold approach for superlinear double phase problems with variable exponents, Ann. Mat. Pura Appl. (4) 203 (2024), no. 2, 605–634. Preprint   Journal   arXiv
  10. S. Carl, V.K. Le, P. Winkert, Multi-valued variational inequalities for variable exponent double phase problems: comparison and extremality results, Adv. Differential Equations, accepted 2023. Preprint   Journal   arXiv
  11. N.S. Papageorgiou, F. Vetro, P. Winkert, Sign changing solutions for critical double phase problems with variable exponent, Z. Anal. Anwend. 42 (2023), no. 1-2, 235–251. Preprint   Journal   
  12. K. Ho, P. Winkert, New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems, Calc. Var. Partial Differential Equations 62 (2023), no. 8, Paper No. 227, 38 pp. Preprint   Journal   arXiv
  13. K. Ho, P. Winkert, Infinitely many solutions to Kirchhoff double phase problems with variable exponents, Appl. Math. Lett. 145 (2023), Paper No. 108783, 8 pp. Preprint   Journal   arXiv
  14. H. Tao, L. Li, P. Winkert, Existence and concentration of solutions for a 1-biharmonic Choquard equation with steep potential well in RN, J. Geom. Anal. 33 (2023), no. 9, Paper No. 276, 27 pp. Preprint   Journal   
  15. F. Vetro, P. Winkert, Nodal solutions for critical Robin double phase problems with variable exponent, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 11, 3333–3349. Preprint   Journal   
  16. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, Existence of ground state solutions for a Choquard double phase problem, Nonlinear Anal. Real World Appl. 73 (2023), 103914, 22 pp. Preprint   Journal   arXiv
  17. Y. Yang, W. Liu, P. Winkert, X. Yan, Existence of solutions for resonant double phase problems with mixed boundary value conditions, Partial Differ. Equ. Appl. 4 (2023), no. 3, Paper No. 18, 17 pp. Preprint   Journal   
  18. S. Zeng, Y. Bai, V.D. Rădulescu, P. Winkert, An inverse problem for a double phase implicit obstacle problem with multivalued terms, ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 30, 23 pp. Preprint   Journal   
  19. U. Guarnotta, R. Livrea, P. Winkert, The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 34 (2023), no. 3, 617–639. Preprint   Journal   arXiv
  20. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On double phase Kirchhoff problems with singular nonlinearity, Adv. Nonlinear Anal. 12 (2023), no. 1, Paper No. 20220312, 24 pp. Preprint   Journal   arXiv
  21. Y. Liu, V.T. Nguyen, P. Winkert, S. Zeng, Coupled double phase obstacle systems involving nonlocal functions and multivalued convection terms, Monatsh. Math. 202 (2023), no. 2, 363–376. Preprint   Journal   
  22. A. Sciammetta, E. Tornatore, P. Winkert, Bounded weak solutions to superlinear Dirichlet double phase problems, Anal. Math. Phys. 13 (2023), no. 2, Paper No. 23, 18 pp. Preprint   Journal   
  23. S. Zeng, N.S. Papageorgiou, P. Winkert, Inverse problems for double-phase obstacle problems with variable exponents, J. Optim. Theory Appl. 196 (2023), no. 2, 666–699. Preprint   Journal   
  24. S. Zeng, L. Gasiński, V.D. Rădulescu, P. Winkert, Anisotropic and isotropic implicit obstacle problems with nonlocal terms and multivalued boundary conditions, Commun. Nonlinear Sci. Numer. Simul. 118 (2023), Paper No. 106997, 34 pp. Preprint   Journal   
  25. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, (p,q)-Equations with negative concave terms, J. Geom. Anal. 33 (2023), no. 1, Paper No. 5, 26 pp. Preprint   Journal   
  26. F. Vetro, P. Winkert, Constant sign solutions for double phase problems with variable exponents, Appl. Math. Lett. 135 (2023), Paper No. 108404, 7 pp. Preprint   Journal   
  27. G. D'Aguì, A. Sciammetta, P. Winkert, On the Fučík spectrum of the p-Laplacian with no-flux boundary condition, Nonlinear Anal. Real World Appl. 69 (2023) 103736, 17 pp. Preprint   Journal   
  28. G. D'Aguì, A. Sciammetta, E. Tornatore, P. Winkert, Parametric Robin double phase problems with critical growth on the boundary, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 6, 1286–1299. Preprint   Journal   
  29. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with multivalued convection and mixed boundary value conditions, Discrete Contin. Dyn. Syst. Ser. B 28 (2023), no. 2, 999–1023. Preprint   Journal   arXiv
  30. S. Zeng, Y. Bai, P. Winkert, J.-C. Yao, Identification of discontinuous parameters in double phase obstacle problems, Adv. Nonlinear Anal. 12 (2023), no. 1, 1–22. Preprint   Journal   
  31. C. Farkas, A. Fiscella, P. Winkert, On a class of critical double phase problems, J. Math. Anal. Appl. 515 (2022), no. 2, 126420, 16 pp. Preprint   Journal   arXiv
  32. F. Vetro, P. Winkert, Existence, uniqueness and asymptotic behavior of parametric anisotropic (p,q)-equations with convection, Appl. Math. Optim. 86 (2022), no. 2, Paper No. 18, 18 pp. Preprint   Journal   
  33. R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On critical double phase Kirchhoff problems with singular nonlinearity, Rend. Circ. Mat. Palermo (2) 71 (2022), no. 3, 1079–1106. Preprint   Journal   
  34. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase obstacle problems with variable exponent, Adv. Differential Equations 27 (2022), no. 9-10, 611–645. Preprint   Journal   
  35. W. Liu, G. Dai, N.S. Papageorgiou, P. Winkert, Existence of solutions for singular double phase problems via the Nehari manifold method, Anal. Math. Phys. 12 (2022), no. 3, Paper No. 75, 25 pp. Preprint   Journal   arXiv
  36. Á. Crespo-Blanco, L. Gasiński, P. Harjulehto, P. Winkert, A new class of double phase variable exponent problems: Existence and uniqueness, J. Differential Equations 323 (2022), 182–228. Preprint   Journal   arXiv
  37. K. Ho, Y.-H. Kim, P. Winkert, C. Zhang, The boundedness and Hölder continuity of solutions to elliptic equations involving variable exponents and critical growth, J. Differential Equations 313 (2022), 503–532. Preprint   Journal   arXiv
  38. S. Zeng, V.D. Rădulescu, P. Winkert, Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions, SIAM J. Math. Anal. 54 (2022), no. 2, 1898–1926. Preprint   Journal   arXiv
  39. W. Liu, P. Winkert, Combined effects of singular and superlinear nonlinearities in singular double phase problems in RN, J. Math. Anal. Appl. 507 (2022), no. 2, 125762, 19 pp. Preprint   Journal   arXiv
  40. Á. Crespo-Blanco, N.S. Papageorgiou, P. Winkert, Parametric superlinear double phase problems with singular term and critical growth on the boundary, Math. Methods Appl. Sci. 45 (2022), no. 4, 2276–2298. Preprint   Journal   arXiv
  41. N.S. Papageorgiou, P. Winkert, A multiplicity theorem for anisotropic Robin equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no. 1, 1–22. Preprint   Journal   arXiv
  42. S. El Manouni, G. Marino, P. Winkert, Existence results for double phase problems depending on Robin and Steklov eigenvalues for the p-Laplacian, Adv. Nonlinear Anal. 11 (2022), no. 1, 304–320. Preprint   Journal   arXiv
  43. N.S. Papageorgiou, P. Winkert, On a class of singular anisotropic (p,q)-equations, Rev. Mat. Complut. 35 (2022), no. 2, 545–571. Preprint   Journal   arXiv
  44. C. Farkas, A. Fiscella, P. Winkert, Singular Finsler double phase problems with nonlinear boundary condition, Adv. Nonlinear Stud. 21 (2021), no. 4, 809–825. Preprint   Journal   arXiv
  45. N.S. Papageorgiou, P. Winkert, Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation, Results Math. 76 (2021), no. 4, Paper No. 169, 20 pp. Preprint   Journal   arXiv
  46. N.S. Papageorgiou, P. Winkert, Positive solutions for singular anisotropic (p,q)-equations, J. Geom. Anal. 31 (2021), no. 12, 11849–11877. Preprint   Journal   arXiv
  47. C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems, J. Differential Equations 286 (2021), 455–473. Preprint   Journal   arXiv
  48. L. Gasiński, P. Winkert, Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold, J. Differential Equations 274 (2021), 1037–1066. Preprint   Journal   arXiv
  49. N.S. Papageorgiou, P. Winkert, Singular Dirichlet (p,q)-equations, Mediterr. J. Math. 18 (2021), no. 4, Paper No. 141, 20 pp. Preprint   Journal   arXiv
  50. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Convergence analysis for double phase obstacle problems with multivalued convection term, Adv. Nonlinear Anal. 10 (2021), no. 1, 659–672. Preprint   Journal   
  51. A. Bahrouni, V.D. Rădulescu, P. Winkert, Small perturbations of Robin problems driven by the p-Laplacian plus a positive potential, Topol. Methods Nonlinear Anal. 57 (2021), no. 2, 663–673. Preprint   Journal   
  52. N.S. Papageorgiou, P. Winkert, (p,q)-Equations with singular and concave convex nonlinearities, Appl. Math. Optim. 84 (2021), no. 3, 2601–2628. Preprint   Journal   arXiv
  53. S. Zeng, L. Gasiński, P. Winkert, Y. Bai, Existence of solutions for double phase obstacle problems with multivalued convection term, J. Math. Anal. Appl. 501 (2021), no. 1, 123997, 12 pp. Preprint   Journal   
  54. N.S. Papageorgiou, P. Winkert, Positive solutions for weighted singular p-Laplace equations via Nehari manifolds, Appl. Anal. 100 (2021), no. 11, 2436–2448. Preprint   Journal   arXiv
  55. A. Bahrouni, V.D. Rădulescu, P. Winkert, Double phase problems with variable growth and convection for the Baouendi-Grushin operator, Z. Angew. Math. Phys. 71 (2020), no. 6, 183. Preprint   Journal   
  56. A. Bahrouni, V.D. Rădulescu, P. Winkert, Robin fractional problems with symmetric variable growth, J. Math. Phys. 61 (2020), no. 10, 101503, 14 pp. Preprint   Journal   arXiv
  57. S. Zeng, Y. Bai, L. Gasiński, P. Winkert, Existence results for double phase implicit obstacle problems involving multivalued operators, Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 176, 18 pp. Preprint   Journal   
  58. G. Marino, P. Winkert, Existence and uniqueness of elliptic systems with double phase operators and convection terms, J. Math. Anal. Appl. 492 (2020), no. 1, 124423, 13 pp. Preprint   Journal   arXiv
  59. A. Bahrouni, V.D. Rădulescu, P. Winkert, A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems, Adv. Nonlinear Stud. 20 (2020), no. 3, 663–674. Preprint   Journal   
  60. G. Marino, P. Winkert, L∞-bounds for general singular elliptic equations with convection term, Appl. Math. Lett. 107 (2020), 106410, 6 pp. Preprint   Journal   arXiv
  61. L. Gasiński, P. Winkert, Constant sign solutions for double phase problems with superlinear nonlinearity, Nonlinear Anal. 195 (2020), 111739, 9 pp. Preprint   Journal   arXiv
  62. Y. Bai, L. Gasiński, P. Winkert, S. Zeng, W1,p versus C1: The nonsmooth case involving critical growth, Bull. Math. Sci. 10 (2020), no. 3, 2050009, 15 pp. Preprint   Journal   
  63. L. Gasiński, P. Winkert, Existence and uniqueness results for double phase problems with convection term, J. Differential Equations 268 (2020), no. 8, 4183–4193. Preprint   Journal   arXiv
  64. G. Marino, P. Winkert, Global a priori bounds for weak solutions of quasilinear elliptic systems with nonlinear boundary condition, J. Math. Anal. Appl. 482 (2020), no. 2, 123555, 19 pp. Preprint   Journal   arXiv
  65. S.A. Marano, P. Winkert, Corrigendum to ''On a quasilinear elliptic problem with convection term and nonlinear boundary condition'' [Nonlinear Anal. 187 (2019), 159–169], Nonlinear Anal. 189 (2019), 111578. Preprint   Journal   
  66. G. D'Aguì, B. Di Bella, P. Winkert, Two positive solutions for nonlinear fourth-order elastic beam equations, Electron. J. Qual. Theory Differ. Equ. 2019, Paper No. 37, 12 pp. Preprint   Journal   
  67. G. Bonanno, G. D'Aguì, P. Winkert, A two critical points theorem for non-differentiable functions and applications to highly discontinuous PDE's, Pure Appl. Funct. Anal. 4 (2019), no. 4, 709–725. Preprint   Journal   
  68. S.A. Marano, P. Winkert, On a quasilinear elliptic problem with convection term and nonlinear boundary condition, Nonlinear Anal. 187 (2019), 159–169. Preprint   Journal   
  69. D. Motreanu, P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78–84. Preprint   Journal   
  70. N.S. Papageorgiou, P. Winkert, Nonlinear systems with Hartman-type perturbations, Monatsh. Math. 190 (2019), no. 2, 389–404. Preprint   Journal   
  71. G. Marino, P. Winkert, Moser iteration applied to elliptic equations with critical growth on the boundary, Nonlinear Anal. 180 (2019), 154–169. Preprint   Journal   arXiv
  72. N.S. Papageorgiou, P. Winkert, Solutions with sign information for nonlinear nonhomogeneous problems, Math. Nachr. 292 (2019), no. 4, 871–891. Preprint   Journal   
  73. N.S. Papageorgiou, P. Winkert, Singular p-Laplacian equations with superlinear perturbation, J. Differential Equations 266 (2019), no. 2-3, 1462–1487. Preprint   Journal   
  74. N.S. Papageorgiou, P. Winkert, Double resonance for Robin problems with indefinite and unbounded potential, Discrete Contin. Dyn. Syst. Ser. S 11, (2018), no. 2, 323–344. Preprint   Journal   
  75. N.S. Papageorgiou, P. Winkert, Asymmetric (p,2)-equations, superlinear at +∞, resonant at -∞, Bull. Sci. Math. 141 (2017), no. 5, 443–488. Preprint   Journal   
  76. S. El Manouni, H. Hajaiej, P. Winkert, Bounded solutions to nonlinear problems in RN involving the fractional Laplacian depending on parameters, Minimax Theory Appl. 2 (2017), no. 2, 265–283. Preprint   Journal   arXiv
  77. N.S. Papageorgiou, P. Winkert, Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities, Positivity 20 (2016), no. 4, 945–979. Preprint   Journal   
  78. P. Winkert, R. Zacher, Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth, Nonlinear Anal. 145 (2016), 1–23. Preprint   Journal   arXiv
  79. N.S. Papageorgiou, P. Winkert, Nonlinear Robin problems with a reaction of arbitrary growth, Ann. Mat. Pura Appl. (4) 195 (2016), no. 4, 1207–1235. Preprint   Journal   
  80. G. Bonanno, G. D'Aguì, P. Winkert, Sturm-Liouville equations involving discontinuous nonlinearities, Minimax Theory Appl. 1 (2016), no. 1, 125–143. Preprint   Journal   
  81. N.S. Papageorgiou, P. Winkert, Nonlinear nonhomogeneous Dirichlet equations with a superlinear nonlinearity, Results Math. 70 (2016), no. 1, 31–79. Preprint   Journal   arXiv
  82. P. Winkert, R. Zacher, Corrigendum to ''A priori bounds for weak solutions to elliptic equations with nonstandard growth'' [Discrete Contin. Dyn. Syst. Ser. S 5 (2012), 865–878], Discrete Contin. Dyn. Syst. Ser. S, published on-line as note, 2015, 1–3. Preprint   Journal   arXiv
  83. S. El Manouni, N.S. Papageorgiou, P. Winkert, Parametric nonlinear nonhomogeneous Neumann equations involving a nonhomogeneous differential operator, Monatsh. Math. 177 (2015), no. 2, 203–233. Preprint   Journal   
  84. N.S. Papageorgiou, P. Winkert, Resonant (p,2)-equations with concave terms, Appl. Anal. 94 (2015), no. 2, 342–360. Preprint   Journal   
  85. P. Winkert, On the boundedness of solutions to elliptic variational inequalities, Set-Valued Var. Anal. 22 (2014), no. 4, 763–781. Preprint   Journal   
  86. G. Bonanno, P. Winkert, Multiplicity results to a class of variational-hemivariational inequalities, Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 493–516. Preprint   Journal   
  87. N.S. Papageorgiou, P. Winkert, On a parametric nonlinear Dirichlet problem with subdiffusive and equidiffusive reaction, Adv. Nonlinear Stud. 14 (2014), no. 3, 747–773. Preprint   Journal   
  88. G. Bonanno, D. Motreanu, P. Winkert, Boundary value problems with nonsmooth potential, constraints and parameters, Dynam. Systems Appl. 22 (2013), no. 2-3, 385–396. Preprint   Journal   
  89. P. Winkert, Multiplicity results for a class of elliptic problems with nonlinear boundary condition, Commun. Pure Appl. Anal. 12 (2013), no. 2, 785–802. Preprint   Journal   
  90. P. Winkert, R. Zacher, A priori bounds for weak solutions to elliptic equations with nonstandard growth, Discrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 4, 865–878. Preprint   Journal   arXiv
  91. D. Motreanu, P. Winkert, On the Fučík spectrum for the p-Laplacian with Robin boundary condition, Nonlinear Anal. 74 (2011), no. 14, 4671–4681. Preprint   Journal   
  92. G. Bonanno, D. Motreanu, P. Winkert, Variational-hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 381 (2011), no. 2, 627–637. Preprint   Journal   
  93. P. Winkert, Multiple solution results for elliptic Neumann problems involving set-valued nonlinearities, J. Math. Anal. Appl. 377 (2011), no. 1, 121–134. Preprint   Journal   
  94. D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition, Matematiche (Catania) 65 (2010), no. 2, 109–119. Preprint   Journal   
  95. P. Winkert, Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems, Bound. Value Probl. 2010, Art. ID 139126, 22 pp. Preprint   Journal   
  96. P. Winkert, Local C1-minimizers versus local W1,p-minimizers of nonsmooth functionals, Nonlinear Anal. 72 (2010), no. 11, 4298–4303. Preprint   Journal   
  97. P. Winkert, L∞-estimates for nonlinear elliptic Neumann boundary value problems, NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 3, 289–302. Preprint   Journal   
  98. P. Winkert, Constant-sign and sign-changing solutions for nonlinear elliptic equations with Neumann boundary values, Adv. Differential Equations 15 (2010), no. 5-6, 561–599. Preprint   Journal   
  99. P. Winkert, Entire extremal solutions for elliptic inclusions of Clarke′s gradient type, Z. Anal. Anwend. 29 (2010), no. 1, 63–75. Preprint   Journal   
  100. S. Carl, P. Winkert, General comparison principle for variational-hemivariational inequalities, J. Inequal. Appl. 2009, Art. ID 184348, 29 pp. Preprint   Journal   
  101. P. Brückmann, P. Winkert, T-symmetrical tensor differential forms with logarithmic poles along a hypersurface section, Int. J. Pure Appl. Math. 46 (2008), no. 1, 111–136. Preprint   Journal   
  102. P. Winkert, Discontinuous variational-hemivariational inequalities involving the p-Laplacian, J. Inequal. Appl. 2007, Art. ID 13579, 11 pp. Preprint   Journal   
Book Contributions
  1. D. Motreanu, P. Winkert, Elliptic problems with nonhomogeneous differential operators and multiple solutions, Chapter 15 in: Mathematics Without Boundaries (Surveys in Pure Mathematics), 357–379, Springer, New York, 2014. PDF   Book chapter
  2. D. Motreanu, P. Winkert, The Fucik spectrum for the negative p-Laplacian with different boundary conditions, Chapter 28 in: Nonlinear Analysis (Stability, Approximation, and Inequalities), 471–485, Springer, New York, 2012. PDF   Book chapter
Theses
  1. P. Winkert, Global a priori bounds and multiplicity results for quasilinear elliptic equations and inequalities, Habilitation thesis, Technische Universität Berlin, Berlin, Germany, November 2015. PDF
  2. P. Winkert, Comparison principles and multiple solutions for nonlinear elliptic problems, PhD thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2009. PDF
  3. P. Winkert, T-symmetrische Tensor-Differentialformen mit logarithmischen Polen, Diploma thesis, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany, July 2006 (available only in German).
Patrick Winkert
Teaching
Teaching Experience
  • Spring 2024
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2023
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Spring 2023
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
  • Fall 2022
    • Lectures 'Analysis III für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2022
    • Lectures 'Analysis II für Mathematikerinnen und Mathematiker'
  • Fall 2021
    • Lectures 'Analysis I für Mathematikerinnen und Mathematiker'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2021
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis II für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with E. Emmrich)
  • Fall 2020
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2020
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler)
  • Fall 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Lectures 'Analysis I und Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2019
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
    • Seminar 'Differentialgleichungen' (with H.-C. Kreusler and R. Kruse)
  • Fall 2018
    • Lectures 'Analysis I für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2018
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2017
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2017
    • Lectures 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
    • Tutorials 'Lineare Algebra und Analytische Geometrie II' (HU Berlin)
  • Fall 2016
    • Lectures 'Funktionalanalysis' (MLU Halle)
    • Lectures 'Dynamische Systeme' (MLU Halle)
    • Tutorials 'Dynamische Systeme' (MLU Halle)
    • Seminar 'Fachseminar Analysis' (with S. Carl, MLU Halle)
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2016
    • Lectures 'Maßtheorie' (MLU Halle)
    • Lectures 'Partielle Differentialgleichungen' (MLU Halle)
  • Fall 2015
    • Lectures 'Lineare Algebra für Ingenieurwissenschaften'
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2015
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2014
    • Tutorials 'Analysis I für Ingenieurwissenschaften'
  • Spring 2014
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Spring 2013
    • Tutorials 'Lineare Algebra für Ingenieurwissenschaften'
  • Fall 2011
    • Lectures 'Funktionalanalysis II'
    • Spring 2011
    • Lectures 'Funktionalanalysis I'
    Fall 2008
    • Tutorials 'Analysis I' (MLU Halle)
Patrick Winkert
Research
Research Interests
  • A priori bounds for elliptic and parabolic problems (equations and inequalities)
  • Comparison principles and multiple solutions for nonlinear elliptic problems
  • Isotropic and anisotropic double phase problems
  • Fucik spectrum of elliptic operators
  • Gradient dependence on the right-hand side (convection term)
  • Morse theory and critical groups
  • Nonhomogeneous operators
  • Nonlinear elliptic and parabolic differential equations and inclusion
  • Nonsmooth variational problems (variational- and hemivariational inequalities)
  • Singular problems
Patrick Winkert
Editorial Activities
Member of the Editorial Board of the following journals:
Guest Editor:
Patrick Winkert
Supervision
Current PhD Projects
  • Ángel Crespo Blanco, Isotropic and anisotropic double phase problems, TU Berlin, BMS Phase II Scholarship.
Supervised Master Theses
  1. Singular double phase Kirchhoff problems with nonlinear Neumann boundary condition, TU Berlin, in preparation.
  2. Existence results for double phase problems via the Nehari manifold, TU Berlin, July 2021.
  3. Constant-sign and sign-changing solutions for nonlinear elliptic equations, TU Berlin, December 2020.
  4. Existenz von Lösungen für quasilineare elliptische Gleichungen mit gradientenabhängigen rechten Seiten, TU Berlin, June 2019.
  5. Lösbarkeit von Variations-Hemivariationsungleichungen mit Hilfe von Ober- und Unterlösung, TU Berlin, April 2016.
Supervised Bachelor Theses
  1. Existenz und Eindeutigkeit für quasilineare elliptische Systeme mit gekoppelten gradientenabhängigen rechten Seiten, TU Berlin, April 2023.
  2. Existenz von Lösungen bei Double-Phase-Problemen mittels kritischer Punkttheorie, TU Berlin, September 2021.
  3. Die Theorie des Bochner-Integrals, TU Berlin, August 2021.
  4. Die Methode von schwacher Ober- und Unterlösung für semilineare, elliptische Randwertprobleme, TU Berlin, January 2021.
  5. Die Nehari-Mannigfaltigkeit zur Lösung einer elliptischen Differentialgleichung, TU Berlin, July 2020.
  6. Der p-Laplace-Operator – Eigenschaften und Lösbarkeit zugehöriger Gleichungen, TU Berlin, January 2020.
  7. Lebesgue- und Sobolev-Räume mit variablen Exponenten, TU Berlin, September 2019.
  8. Origami: Definition in einem analytischen Kontext und Lösen spezieller Dirichlet-Probleme, MLU Halle, June 2018.
  9. Nonlinear eigenvalue problems for nonhomogeneous differential operators, MLU Halle, October 2017.
  10. Die Gelfandsche Darstellungstheorie, MLU Halle, May 2017.
  11. Das Fučík-Spektrum des p-Laplace-Operators mit Steklov-Randbedingung, TU Berlin, May 2016.
  12. De Giorgi-Iteration für quasilineare, elliptische Gleichungen mit Neumann-Randbedingung, TU Berlin, December 2015.
  13. The eigenvalue problem of the p-Laplacian with Robin boundary condition, TU Berlin, February 2013.
  14. Die Methode von Ober- und Unterlösung für nichtlineare, elliptische Gleichungen, TU Berlin, February 2013.
  15. A priori bounds for elliptic problems with nonlinear boundary condition, TU Berlin, June 2012.

Patrick Winkert
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