Approximation by solutions of elliptic equations
type: Item
instance of: scholarly article
title: Approximation by solutions of elliptic equations
zbMATH Open document ID: 0593.35080
DOI: 10.4171/ZAA/180
author: Uwe Hamann
author: Günther Wildenhain
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1986-01-01T00:00:00Z
review text: Let \(\Omega\) be a bounded smooth domain in \({\mathbb{R}}^ n\), \(\Gamma\) a closed smooth (n-1)-dimensional surface with boundary in the interior of \(\Omega\), V an open subset of \(\partial \Omega\), L an 2m-order properly elliptic operator with smooth coefficients, and \((B_ 1,...,B_ m)\) a normal system of boundary operators on \(\partial \Omega\). The author proves that the set of all \(C^{\infty}({\bar \Omega})\)-solutions of \(Lu=0\), \(B_ ju|_{\partial \Omega}=0\) on \(\partial \Omega \setminus V\), is dense in \(W_ p^{2m-1/p}(\Gamma)\) for \(p>1\).
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 3953403
zbMATH Keywords: operator equations
zbMATH Keywords: Sobolev space
zbMATH Keywords: properly elliptic operator
reviewed by: Jürgen Appell
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3953403