P. Tolksdorf

activity

20132022

most citedThe Stokes operator in two-dimensional bounded Lipschitz domains

9 citations · 16 across the 12 of their papers we have counts for

collaborators

14 papers

math.AP2022★ 9 cited

The Stokes operator in two-dimensional bounded Lipschitz domains

Fabian Gabel, Patrick Tolksdorf

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $Ω$ subject to homogeneous Dirichlet boundary conditions. We prove $L^{p}$ -resolvent e…

math.AP2022

Critical regularity issues for the compressible Navier--Stokes system in bounded domains

Raphaël Danchin, Patrick Tolksdorf

We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $R^{d}$ (with $d \geq 2$ ). In a critical regularity setting, we establish local w…

math.AP2021

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

Patrick Tolksdorf

We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on $L_{σ}^{2} (R^{d})$ . Such estimates are well-kn…

math.AP2020

A non-local approach to the generalized Stokes operator with bounded measurable coefficients

Patrick Tolksdorf

We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L_{σ}^{p} (R^{d})$ , $d \geq 2$ , for $\lvert 1 / p - 1 / 2 \rvert < 1…

math.AP2020

Lorentz spaces in action on pressureless systems arising from models of collective behavior

Raphaël Danchin, Piotr Boguslaw Mucha, Patrick Tolksdorf

We are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective be…

math.AP2019

The Stokes resolvent problem: Optimal pressure estimates and remarks on resolvent estimates in convex domains

Patrick Tolksdorf

The Stokes resolvent problem $λ u - Δ u + \nabla ϕ = f$ with $div (u) = 0$ subject to homogeneous Dirichlet or homogeneous Neumann-type boundary conditions is investigated. In…

math.CA2019★ 1 cited

Extendability of functions with partially vanishing trace

Sebastian Bechtel, Russell M. Brown, Robert Haller-Dintelmann +1

Let $Ω \subseteq R^{d}$ be open and $D \subseteq \partial Ω$ be a closed part of its boundary. Under very mild assumptions on $Ω$ , we construct a bounded Sobolev extension oper…

math.AP2019

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory

Patrick Tolksdorf, Keiichi Watanabe

We show that the Stokes operator defined on $L_{σ}^{p} (Ω)$ for an exterior Lipschitz domain $Ω \subset R^{n}$ $(n \geq 3)$ admits maximal regularity provided that $p$ s…

math.AP2017★ 3 cited

Nematic Liquid Crystals in Lipschitz domains

Anupam Pal Choudhury, Amru Hussein, Patrick Tolksdorf

We consider the simplified Ericksen-Leslie model in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming…

math.AP2017★ 2 cited

Strong Time Periodic Solutions to the Bidomain Equations with FitzHugh-Nagumo Type Nonlinearities

Matthias Hieber, Naoto Kajiwara, Klaus Kress +1

Consider the bidomain equations subject to ionic transport described by the models of FitzHugh-Nagumo, Aliev-Panfilov, or Rogers-McCulloch. It is proved that this set of equations…

math.AP2016

$R$ -sectoriality of higher-order elliptic systems on general bounded domains

Patrick Tolksdorf

On bounded domains $Ω \subset R^{d}, d \geq 2$ , reaching far beyond the scope of Lipschitz domains, we consider an elliptic system of order $2 m$ in divergence form with com…

math.CA2016★ 1 cited

Characterizations of Sobolev Functions that vanish on a part of the boundary

Moritz Egert, Patrick Tolksdorf

Let $Ω$ be a bounded domain in R n with a Sobolev extension property around the complement of a closed part D of its boundary. We prove that a function u $\in$ W 1,p ( $Ω$ ) vanishes…

math.FA2013

The Kato Square Root Problem for Mixed Boundary Conditions

Moritz Egert, Robert Haller-Dintelmann, Patrick Tolksdorf

We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical expo…

math.FA2013

The Kato Square Root Problem follows from an Extrapolation Property of the Laplacian

Moritz Egert, Robert Haller-Dintelmann, Patrick Tolksdorf

On a domain $Ω \subseteq R^{d}$ we consider second order elliptic systems in divergence form with bounded complex coefficients, realized via a sesquilinear form with domain $…

The Stokes operator in two-dimensional bounded Lipschitz domains

Critical regularity issues for the compressible Navier--Stokes system in bounded domains

On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

A non-local approach to the generalized Stokes operator with bounded measurable coefficients

Lorentz spaces in action on pressureless systems arising from models of collective behavior

The Stokes resolvent problem: Optimal pressure estimates and remarks on resolvent estimates in convex domains

Extendability of functions with partially vanishing trace

The Navier--Stokes equations in exterior Lipschitz domains: Lp-theory

Nematic Liquid Crystals in Lipschitz domains

Strong Time Periodic Solutions to the Bidomain Equations with FitzHugh-Nagumo Type Nonlinearities

R-sectoriality of higher-order elliptic systems on general bounded domains

Characterizations of Sobolev Functions that vanish on a part of the boundary

The Kato Square Root Problem for Mixed Boundary Conditions

The Kato Square Root Problem follows from an Extrapolation Property of the Laplacian

The Navier--Stokes equations in exterior Lipschitz domains: $L^{p}$ -theory

$R$ -sectoriality of higher-order elliptic systems on general bounded domains