Jun. Prof. Dr. Patrick Tolksdorf




ptolksdo (at) uni-mainz.de
+49 6131 39-26099
Download here


WS 2022/2023 Vorlesung: Evolutionsgleichungen
WS 2022/2023 Lokaler Koordinator ISEM26: Graphs and Discrete Dirichlet Spaces
SS 2022 Vorlesung: Analysis 3
WS 2021/2022 Vorlesung: Analysis 2
WS 2021/2022 Lokaler Koordinator ISEM25: Spectral theory for Operators and Semigroups
SS 2021 Vorlesung: Analysis 1
WS 2020/2021 Vorlesung: Harmonische Analysis und Partielle Differentialgleichungen
WS 2020/2021 Hauptseminar: Harmonische Analysis und Partielle Differentialgleichungen
SS 2020 Vorlesung: Harmonische Analysis
WS 2019/2020 Vorlesung: Halbgruppenmethoden für die Navier-Stokes-Gleichungen
WS 2019/2020 Proseminar: Kuriositäten der Analysis
SS 2017 Vorlesung: Navier-Stokes-Gleichungen (an der TU Darmstadt)

Research Interests

My research mainly focuses on the analysis non-smooth problems from fluid mechanics. I am particularly interested in operator theoretic properties as generator properties of analytic semigroups as well as maximal regularity properties in different non-smooth situations.

Here is a list of my publications followed by a list of recent preprint:

Articles (published)

The Stokes operator in two-dimensional bounded Lipschitz domains. With F. Gabel. J. Differential Eq. 340 (2022), 227-272.

On the \(L^p\)-theory of second-order elliptic operators in divergence form with complex coefficients. With A. F. M. ter Elst, R. Haller-Dintelmann, and J. Rehberg. J. Evol. Equ. 21 (2021), no. 4, 3963-4003.

\(L^p\)-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients. J. Evol. Equ. 21 (2021), no. 3, 3129-3151.

Lorentz spaces in action on pressureless systems arising from models of collective behavior. With R. Danchin and P. B. Mucha. J. Evol. Equ. 21 (2021), no. 3, 3103-3127.

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients. J. Elliptic Parabol. Equ. 7 (2021), no. 2, 323-340.

Strong time periodic solutions to the bidomain equations with FitzHugh-Nagumo type nonlinearities. With M. Hieber, N. Kajiwara, and K. Kress, Ann. Mat. Pura. Appl. (4) 199 (2020), no. 6, 2435-2457.

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.

The Navier-Stokes equations in exterior Lipschitz domains: \(L^p\)-theory. With K. Watanabe. J. Differential Equations 269 (2020), no. 7, 5765-5801.

Nematic liquid crystals in Lipschitz domains. With A. P. Choudhury and A. Hussein, SIAM J. Math. Anal. 50 (2018), no. 4, 4282-4310.

\(R\)-sectoriality of higher-order elliptic operators on general bounded domains. J. Evol. Equ. 18 (2018), no. 2, 323-349.

On the \(L^p\)-theory of the Navier-Stokes equations in three-dimensional bounded Lipschitz domains. Math. Ann. 371 (2018), no. 1-2, 445-460.

Characterizations of Sobolev functions that vanish on a part of the boundary. With M. Egert, Discrete Contin. Dyn. Syst. Ser. S 10 (2017), no. 4, 729-743.

The Kato square root problem follows from an extrapolation property of the Laplacian. With M. Egert and R. Haller-Dintelmann, Publ. Math. 60 (2016), no. 2, 451-483.

The Kato square root problem for mixed boundary conditions. With M. Egert and R. Haller-Dintelmann, J. Funct. Anal. 267 (2014), no. 5, 1419-1461.

Articles (preprints)

Critical regularity issues for the compressible Navier-Stokes system in bounded domains. With R. Danchin. Available at arXiv:2201.03823. Accepted at Math. Ann.

A non-local approach to the generalized Stokes operator with bounded measurable coefficients. Available at arXiv:2011.13771

Free Boundary Problems via Da Prato - Grisvard Theory. With R. Danchin, M. Hieber, and P. B. Mucha. Availabe at arXiv:2011.07918v2

Extendability of functions with partially vanishing trace. With S. Bechtel, R. M. Brown, and R. Haller-Dintelmann. Available at arXiv:1910.06009


On the \(L^p\)-theory of the Navier-Stokes equations on Lipschitz domains. Technische Universität Darmstadt, Darmstadt, 2017.