The Dirichlet problem for the Stokes system on Lipschitz domains
type: Item
instance of: scholarly article
title: The Dirichlet problem for the Stokes system on Lipschitz domains
zbMATH Open document ID: 0685.35085
DOI: 10.1215/S0012-7094-88-05734-1
author: C. E. Kenig
author: Eugene B. Fabes
author: Gregory Verchota
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The purpose of this paper is to study the solvability of the Dirichlet problem for the Stokes system of linearized hydrostatics on an arbitrary domain. The authors also present existence and uniqueness with optimal error estimate of the developed method. The authors' result is proven by establishing the relevant Rellich formulas for Stokes operators.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 4122498
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Stokes system
zbMATH Keywords: hydrostatics
zbMATH Keywords: error estimate
zbMATH Keywords: Rellich formulas
reviewed by: Prabhat Kumar Mahanti
MaRDI profile type: Publication
cites work: Cauchy integrals on Lipschitz curves and related operators
cites work: Q3748546
cites work: L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
cites work: Estimates of harmonic measure
cites work: On the Poisson integral for Lipschitz and $C^{1}$-domains
cites work: Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
cites work: The Dirichlet problem for the biharmonic equation in a Lipschitz domain
cites work: Boundary value problems for the systems of elastostatics in Lipschitz domains
cites work: Q3748631
cites work: Q4137515
cites work: Potential techniques for boundary value problems on \(C^1\)-domains
cites work: The Dirichlet problem in non-smooth domains
cites work: The Neumann problem on Lipschitz domains
cites work: Q3339370
cites work: Q3722946
cites work: Q3762712
cites work: Q5733282
cites work: Q3094428
cites work: Darstellung der Eigenwerte von \(\Delta u+\lambda u=0\) durch ein Randintegral
cites work: Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
full work available at URL: s0012-7094-88-05734-1
OpenAlex ID: W1509285559
description: scientific article; zbMATH DE number 4122498