A priori conditions for linear second order elliptic equations in two variables in unbounded domains
type: Item
instance of: scholarly article
title: A priori conditions for linear second order elliptic equations in two variables in unbounded domains
zbMATH Open document ID: 0551.35023
author: Luciana Sgambati
published in: Ricerche di Matematica
publication date: 1983-01-01T00:00:00Z
review text: The author considers a homogeneous Dirichlet problem in an unbounded plane domain A related to a second-order uniformly elliptic linear operator L. The coefficients of L are assumed to be measurable and bounded and to admit limits as x tends to infinity. Taking advantage of a basic result by \textit{G. Talenti} [Matematiche 21, 339-376 (1966; Zbl 0149.074)], and introducing suitable classes of domains and weights g, the author proves, via some apriori estimates, that the operator L, restricted to the Sobolev weighted space \(W^ 2_ 0(A,g(x)dx),\) has a finite dimensional kernel and a closed range.
reviewed by: Alfredo Lorenzi
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 3877614
zbMATH Keywords: homogeneous Dirichlet problem
zbMATH Keywords: apriori estimates
zbMATH Keywords: Sobolev weighted space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3877614