Dirichlet problem for a linear elliptic equation in unbounded domains with \(L^ 2\)-boundary data
type: Item
instance of: scholarly article
title: Dirichlet problem for a linear elliptic equation in unbounded domains with \(L^ 2\)-boundary data
zbMATH Open document ID: 0557.35037
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1984-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107942
review text: The purpose of the paper is to investigate the solvability in \(W^{1,2}_{loc}(\Omega)\) of the Dirichlet problem \(Lu=f\) in \(\Omega\), \(u|_{\partial \Omega}=\phi\), where L is a linear uniformly elliptic operator of order two, \(\Omega\) is the half-space \(\{x=(x_ 1,...,x_ n)\in {\mathbb{R}}^ n| x_ n>0\}\) or the complement to \({\mathbb{R}}^ n\) of a bounded closed set, f is measurable and bounded on \(\Omega\), \(\phi\in\) \(L^ 2(\partial \Omega)\). The boundary \(\partial \Omega\) is assumed to be of class \(C^ 2\) and the boundary condition \(u|_{\partial \Omega}=\phi\) means that \[ \lim_{\delta \to 0}\int_{\partial \Omega}[u(x-\delta \nu (x))-\phi (x)]^ 2dx=0, \] where \(\nu\) (x) is the outward normal to \(\partial \Omega\) at x.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3888156
zbMATH Keywords: unbounded domains
zbMATH Keywords: solvability
zbMATH Keywords: Dirichlet problem
author: Jan Chabrowski
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3888156