Department of Mathematics
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Institute for Analysis
Workgroup Functional Analysis
Dr. Patrick Tolksdorf
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Dr. Patrick Tolksdorf

Current Events

Date Event
2.9.2025, 8:00 - 10:00 Exam Analysis 2
3.9.2025, 8:00 - 13:00 Exam Higher Mathematics I/II for Comuter Science
3.9.2025, 14:00 - 16:00 Exam Analysis 1
4.9.2025, 8:00 - 10:00 Exam Analysis 3

Current List of Courses

Semester Titel Links Typ
Sommersemester 2025 Numerical Methods (Electrical Engineering, Meteorology, Remote Sensing, Geoinformatics) Vorlesung (V)
Tutorial for 0180300 Übung (Ü)
Höhere Mathematik II (Analysis) für die Fachrichtung Informatik Vorlesung (V)
Übungen zu 0186800 Übung (Ü)
Semester Titel Typ
Winter Semester 2024/25 Internetseminar `Ergodic Structure Theory and Applications' Lecture
Höhere Mathematik I (Analysis) für die Fachrichtung Informatik Lecture
Proseminar (Analysis) Proseminar
Summer Semester 2024 Semigroup Theory for the Navier-Stokes Equations Lecture
Höhere Mathematik II (Analysis) für die Fachrichtung Informatik Lecture
Summer Semester 2023 Harmonische Analysis Lecture
Distributionentheorie Seminar

Research

Publications

Published Articles

  1. R. Danchin and P. Tolksdorf. Critical regularity issues for the compressible Navier-Stokes system in bounded domains. Math. Ann. 387 (2023), no. 3-4, 1903-1959.
  2. F. Gabel and P. Tolksdorf. The Stokes operator in two-dimensional bounded Lipschitz domains. J. Differential Equations 340 (2022), 227-272.
  3. A. F. M. ter Elst, R. Haller-Dintelmann, J. Rehberg and P. Tolksdorf. On the L^p-theory for second-order elliptic operators in divergence form with complex coefficients. J. Evol. Equ. 21 (2021), no. 4, 3963-4003.
  4. P. Tolksdorf. L^p-extrapolation of non-local operators: maximal regularity of elliptic integrodifferential operators with measurable coefficients. J. Evol. Equ. 21 (2021), no. 3, 3129-3151.
  5. R. Danchin, P. B. Mucha and P. Tolksdorf. Lorentz spaces in action on pressureless systems arising from models of collective behavior. J. Evol. Equ. 21 (2021), no. 3, 3103-3127.
  6. P. Tolksdorf. On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients. J. Elliptic Parabol. Equ. 7 (2021), no. 2, 323-340.
  7. M. Hieber, N. Kajiwara, K. Kress and P. Tolksdorf. The periodic version of the Da Prato–Grisvard theorem and applications to the bidomain equations with FitzHugh-Nagumo transport. Ann. Mat. Pura Appl. (4) 199 (2020), no. 6, 2435-2457.
  8. P. Tolksdorf. The Stokes resolvent problem: optimal pressure estimates and remarks on resolvent estimates in convex domains. Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 154, 40 pp.
  9. P. Tolksdorf and K. Watanabe. The Navier-Stokes equations in exterior Lipschitz domains: L^p-theory. J. Differential Equations 269 (2020), no. 7, 5765-5801.
  10. A. Pal Choudhury, A. Hussein and P. Tolksdorf. Nematic liquid crystals in Lipschitz domains. SIAM J. Math. Anal. 50 (2018), no. 4, 4282-4310.
  11. P. Tolksdorf. R-sectoriality of higher-order elliptic systems on general bounded domains. J. Evol. Equ. 18 (2018), no. 2, 323-349.
  12. P. Tolksdorf. On the L^p-theory of the Navier-Stokes equations on three-dimensional bounded Lipschitz domains. Math. Ann. 371 (2018), no. 1-2, 445-460.
  13. M. Egert and P. Tolksdorf. Characterizations of Sobolev functions that vanish on a part of the boundary. Discrete Contin. Dyn. Syst. Ser. S 10 (2017), no. 4, 729-743.
  14. M. Egert, R. Haller-Dintelmann and P. Tolksdorf. The Kato square root problem follows from an extrapolation property of the Laplacian. Publ. Mat. 60 (2016), no. 2, 451-483.
  15. M. Egert, R. Haller-Dintelmann and P. Tolksdorf. The Kato square root problem for mixed boundary conditions. J. Funct. Anal. 267 (2014), no. 5, 1419-1461.

Preprints

  1. M. Hieber, H. Kozono, S. Monniaux and P. Tolksdorf. Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains. Available here.
  2. L. Haardt and P. Tolksdorf. On Kato's Square Root Property for the Generalized Stokes Operator. Available here.
  3. P. Tolksdorf. A non-local approach to the generalized Stokes operator with bounded measurable coefficients. Available here.
  4. R. Danchin, M. Hieber, P. B. Mucha and P. Tolksdorf. Free Boundary Problems via Da Prato-Grisvard Theory. Available here. Published soon in the Memoirs of the AMS.
  5. S. Bechtel, R. Brown, R. Haller-Dintelmann and P. Tolksdorf. Extendability of functions with partially vanishing trace. Available here. Published soon in the Annales de l'Institut Fourier.

Lecture Notes of the 27. Internet Seminar

  1. M. Egert, R. Haller, S. Monniaux und P. Tolksdorf. Harmonic Analysis Techniques for Elliptic Operators. Available here.

Dissertation

  1. P. Tolksdorf. On the L^p-theory of the Navier-Stokes equation on Lipschitz domains. Technische Universität Darmstadt, 2017. Available here.

Organized Events

  1. Workshop on Harmonic Analysis and Fluid Flows from June 16 to 20, 2025, in Bad Herrenalb, Germany. Organized with D. Frey.
  2. Workshop on Maximal Regularity and Related Topics from April 01 to 04, 2025, in Frankenstein, Germany. Organized with A. Hussein.
  3. 27. international Internet Seminar on Harmonic Analysis Techniques for Elliptic Operators from October 2023 to June 2024 with final workshop from June 17 to 21, 2024, at CIRM in Luminy, Marseille. Organized with M. Egert, R. Haller and S. Monniaux.
  4. 7. MathFlows conference from December 05 to 09, 2022, at CIRM in Luminy, Marseille. Organized with R. Danchin and P. B. Mucha.

Other Activities

Jointly with Amru Hussein I am running a DFG network with the title "Maximal Regularity Methods in Mathematical Fluid Mechanics".