The \(L^p\) regularity problem for the Stokes system on Lipschitz domains

DOI10.1016/j.jde.2015.02.041zbMath1319.35159OpenAlexW2041933433MaRDI QIDQ2344802

Joel Kilty, Jun Geng

Publication date: 18 May 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.02.041

zbMATH Keywords

Stokes systemLipschitz domainregularity problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30)

Related Items (max. 100)

The \(L^{p}\) Robin problem for Laplace equations in Lipschitz and (semi-)convex domains ⋮ Lp Neumann problem for some Schrödinger equations in (semi-)convex domains ⋮ Higher order fractional differentiability for the stationary Stokes system ⋮ On the \(\mathrm {L}^p\)-theory of the Navier-Stokes equations on three-dimensional bounded Lipschitz domains ⋮ Convergence rates and \(W^{1,p}\) estimates in homogenization theory of Stokes systems in Lipschitz domains ⋮ Resolvent estimates in \(L ^{p }\) for the Stokes operator in Lipschitz domains ⋮ Necessary and sufficient conditions for the solvability of the Neumann and the regularity problems in \(L^p\) of some Schrödinger equations on Lipschitz domains ⋮ Homogenization of some degenerate pseudoparabolic variational inequalities ⋮ Weighted \(L^p\) boundary value problems for Laplace's equation on (semi-)convex domains ⋮ Lq-Estimates for stationary Stokes system with coefficients measurable in one direction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO
• A bilinear estimate for biharmonic functions in Lipschitz domains
• Uniform \(W^{1,p}\) estimates for systems of linear elasticity in a periodic medium
• Existence, uniqueness and \(L^ q\)-estimates for the Stokes problem in an exterior domain
• \(W^{1,p}\) estimates for elliptic problems with Neumann boundary conditions in Lipschitz domains
• Layer potentials and boundary value problems for elliptic systems in Lipschitz domains
• The \(L^p\) Dirichlet problem for elliptic systems on Lipschitz domains
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• The Dirichlet problem for the biharmonic equation in a Lipschitz domain
• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• On the existence and regularity of the solution of Stokes problem in arbitrary dimension
• Estimates of harmonic measure
• A maximum principle for biharmonic functions in Lipschitz and \(C^ 1\) domains
• On the Stokes problem in Lipschitz domains
• Area integral estimates for higher order elliptic equations and systems
• The stationary Navier-Stokes system in nonsmooth manifolds: the Poisson problem in Lipschitz and \(C^{1}\) domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
• Necessary and sufficient conditions for the solvability of the \(L^p\) Dirichlet problem on Lipschitz domains
• The \(L^{p}\) boundary value problems on Lipschitz domains
• On estimates of biharmonic functions on Lipschitz and convex domains
• Su un problema al contorno relativo al sistema di equazioni di Stokes
• The 𝐿^{𝑝} regularity problem on Lipschitz domains
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On the Poisson integral for Lipschitz and $C^{1}$-domains
• The Neumann problem on Lipschitz domains
• The Dirichlet Problem in L p for the Biharmonic Equation on Lipschitz Domains
• A Note on the Dirichlet Problem for the Stokes System in Lipschitz Domains
• Estimates for the Stokes operator in Lipschitz domains
• The $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains

This page was built for publication: The \(L^p\) regularity problem for the Stokes system on Lipschitz domains