Jun. Prof. Dr. Patrick Tolksdorf

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ptolksdo (at) uni-mainz.de
+49 6131 39-26099
2413
04-628

Lehre

SS 2021 phantom phantom

WS 2020/2021
phantom

WS 2020/2021

SS 2020

WS 2019/2020

WS 2019/2020

SS 2017

Vorlesung: Analysis 1 (digital) Für weitere Informationen nehmen Sie bitte an der Info-Veranstaltung am 06. April teil. Den Link finden Sie in Jogustine unter der Veranstaltung "Einführungsveranstaltung für Studienanfänger"

Vorlesung: Harmonische Analysis und Partielle Differentialgleichungen (digital, bitte über jogustine anmelden und dann ins zugehörige Moodle schauen!)

Hauptseminar: Harmonische Analysis und Partielle Differentialgleichungen

Vorlesung: Harmonische Analysis (digital)

Vorlesung Halbgruppenmethoden für die Navier-Stokes-Gleichungen

Proseminar: Kuriositäten der Analysis

Vorlesung: Navier-Stokes-Gleichungen (an der TU Darmstadt)

Articles (published)

Lorentz spaces in action on pressureless systems arising from models of collective behavior. With R. Danchin and P. B. Mucha. Accepted at J. Evol. Equ. Online first: https://link.springer.com/article/10.1007/s00028-021-00668-4

L^p-extrapolation of non-local operators: Maximal regularity of elliptic integrodifferential operators with measurable coefficients. Accepted at J. Evol. Equ. Online first: https://link.springer.com/article/10.1007/s00028-020-00609-7

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)

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients. Available on arXiv:2103.03226

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:2011.07918

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 second-prder elliptic operators in divergence form with complex coefficients. With A. F. M. ter Elst, R. Haller-Dintelmann, and J. Rehberg. Available at arXiv:1903.06692

Dissertation

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