Dr. rer. nat. Patrick Tolksdorf

Dr. rer. nat. Patrick Tolksdorf

  • Englerstraße 2
    76131 Karlsruhe

Current Courses

Titel Links Typ
Wintersemester 2025/26
Internetseminar für Evolutionsgleichungen Vorlesung (V)
Proseminar (Analysis) Proseminar (PS)
Höhere Mathematik I (Analysis) für die Fachrichtung Informatik Vorlesung (V)
Übungen zu 0133000 (Höhere Mathematik I (Analysis) für Informatik) Übung (Ü)
Sommersemester 2025
Numerical Methods (Electrical Engineering, Meteorology, Remote Sensing, Geoinformatics) Vorlesung (V)
Tutorial for 0180300 (Numerical Methods (Electrical Engineering, Meteorology, Remote Sensing, Geoinformatics)) Übung (Ü)
Höhere Mathematik II (Analysis) für die Fachrichtung Informatik Vorlesung (V)
Übungen zu 0186800 (Höhere Mathematik II (Analysis) für Informatik) Übung (Ü)
Wintersemester 2024/25
Internetseminar für Evolutionsgleichungen Vorlesung (V)
Proseminar (Analysis) Proseminar (PS)
Höhere Mathematik I (Analysis) für die Fachrichtung Informatik Vorlesung (V)
Übungen zu 0133000 (Höhere Mathematik I (Analysis) für Informatik) Übung (Ü)

Research

Publications
Published Articles
  1. R. Danchin, M. Hieber, P. B. Mucha and P. Tolksdorf. Free Boundary Problems via Da Prato-Grisvard Theory. Mem. Amer. Math. Soc. 311 (2025), no. 1578, v+148 pp.
  2. 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.
  3. F. Gabel and P. Tolksdorf. The Stokes operator in two-dimensional bounded Lipschitz domains. J. Differential Equations 340 (2022), 227-272.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. A. Pal Choudhury, A. Hussein and P. Tolksdorf. Nematic liquid crystals in Lipschitz domains. SIAM J. Math. Anal. 50 (2018), no. 4, 4282-4310.
  12. P. Tolksdorf. R-sectoriality of higher-order elliptic systems on general bounded domains. J. Evol. Equ. 18 (2018), no. 2, 323-349.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  2. L. Haardt and P. Tolksdorf. On Kato's Square Root Property for the Generalized Stokes Operator.
  3. P. Tolksdorf. A non-local approach to the generalized Stokes operator with bounded measurable coefficients. Published soon in Calculus of Variations and Partial Differential Equations.
  4. S. Bechtel, R. Brown, R. Haller-Dintelmann and P. Tolksdorf. Extendability of functions with partially vanishing trace. 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. Conference on Mathematical Fluid Mechanics and Related Topics from March 09 to 13, 2026, in Regensburg. Organized with H. Abels, R. Höfer, A. Hussein, A. Matioc and J. Sauer.
  2. Workshop on Harmonic Analysis and Fluid Flows from June 16 to 20, 2025, in Bad Herrenalb, Germany. Organized with D. Frey.
  3. Workshop on Maximal Regularity and Related Topics from April 01 to 04, 2025, in Frankenstein, Germany. Organized with A. Hussein.
  4. 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.
  5. 7. MathFlows conference from December 05 to 09, 2022, at CIRM in Luminy, Marseille. Organized with R. Danchin and P. B. Mucha.

Other Activities

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