Jun. Prof. Dr. Patrick Tolksdorf

Kontakt

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Kontakt

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

Lehre

WS 2020/2021
phantom

WS 2020/2021

SS 2020

WS 2019/2020

WS 2019/2020

SS 2017

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)

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)

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. Available at arXiv:2005.05603v2

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.