Patrick Winkert

Professor Patrick Winkert is a faculty member at the Institute of Mathematics within the Faculty of Mathematics and Natural Sciences at Technische Universität Berlin. He has been serving as a Professor at TU Berlin since 2025, following his position as Associate Professor (Privatdozent) from 2016 to 2025. His academic journey includes substitute professorships at Martin-Luther-Universität Halle-Wittenberg (MLU Halle) and Humboldt-Universität zu Berlin (HU Berlin), as well as postdoctoral work at TU Berlin after completing his PhD at MLU Halle.

Winkert's research focuses on nonlinear functional analysis and partial differential equations, with particular expertise in double phase problems, elliptic and parabolic equations, variational methods, and critical point theory. His work spans theoretical developments and applications in mathematical analysis. His research interests include a priori bounds for elliptic and parabolic problems, comparison principles, multiple solutions for nonlinear elliptic problems, isotropic and anisotropic double phase problems, the Fucik spectrum of elliptic operators, gradient dependence on the right-hand side, Morse theory, nonhomogeneous operators, and nonsmooth variational problems.

His publication record is extensive, with over 120 refereed journal articles, two monographs with N.S. Papageorgiou titled 'Applied Nonlinear Functional Analysis. An Introduction,' and several book chapters. His recent work (2025-2026) predominantly focuses on logarithmic double phase problems, Schrödinger equations, eigenvalue problems for the (p,q)-Laplacian, and various aspects of variational-hemivariational inequalities. These publications appear in prestigious journals including Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, and Nonlinear Analysis.

Winkert serves on the editorial boards of several prominent journals: Applicable Analysis (Taylor & Francis, since 2021), Applied Mathematics Letters (Elsevier, since 2023, as Associate Editor since 2024), and Boundary Value Problems (Springer, since 2020). He has also served as Guest Editor for special issues in Nonlinear Analysis - Real World Applications and Discrete and Continuous Dynamical Systems.

He has supervised numerous graduate students, including PhD candidate Ángel Crespo Blanco who completed his dissertation on 'Double phase elliptic problems: existence and multiplicity results' in September 2024. His supervision extends to multiple Master's and Bachelor's theses focusing on various aspects of double phase problems, the Nehari manifold, sign-changing solutions, and other topics in nonlinear analysis.

Winkert teaches a range of mathematics courses at TU Berlin, primarily focusing on analysis and linear algebra for engineering students, as well as more advanced courses for mathematics majors including Functional Analysis and Partial Differential Equations.