An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions
type: Item
instance of: scholarly article
title: An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions
zbMATH Open document ID: 0734.35077
DOI: 10.1007/BF02568383
author: Werner Varnhorn
published in: Manuscripta Mathematica
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155594
review text: The paper gives a representation of the solution of the resolvent problem for the Stokes-system \[ (\lambda I-\Delta)u+\nabla \pi =f,\quad div u=0,\quad u|_{\partial \Omega}=0 \] on bounded or exterior domains \(\Omega \subset {\mathbb{R}}^ 3\) by potential theoretic methods. This can be found also in \textit{P. Deuring} [Math. Methods Appl. Sci. 13, 323-333, and 335-349 (1990; Zbl 0726.35098 and Zbl 0726.35099)] together with explicit estimates in \(L_ p\)-spaces. The paper ends with boundary integral equations for the case \(f=0\) and Dirichlet- or Neumann type boundary conditions.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4214528
zbMATH Keywords: resolvent problem
zbMATH Keywords: Stokes-system
zbMATH Keywords: potential theoretic methods
zbMATH Keywords: boundary integral equations
reviewed by: Michael Wiegner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214528