The Poisson equation in homogeneous Sobolev spaces
type: Item
instance of: scholarly article
title: The Poisson equation in homogeneous Sobolev spaces
zbMATH Open document ID: 1155.35318
DOI: 10.1155/S0161171204308094
author: Werner Varnhorn
author: Tatiana S. Samrowski
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/55079
review text: Summary: We consider Poisson's equation in an \(n\)-dimensional exterior domain \(G\) \((n \geq 2)\) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain \(L^q(G)\)-spaces there exists a solution in the homogeneous Sobolev space \(S^{2,q}(G)\), containing functions being local in \(L^q(G)\) and having second-order derivatives in \(L^q(G)\) Concerning the uniqueness of this solution we prove that the corresponding nullspace has the dimension \(n+1\), independent of \(q\).
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 2171560
MaRDI profile type: Publication
OpenAlex ID: W2121106507
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description: scientific article; zbMATH DE number 2171560