On the Dirichlet problem with an asymptotic condition for an elliptic system strongly degenerate at a point
type: Item
instance of: scholarly article
title: On the Dirichlet problem with an asymptotic condition for an elliptic system strongly degenerate at a point
zbMATH Open document ID: 1017.35035
DOI: 10.1023/A:1013816706017
author: Yanyan Li
published in: Lithuanian Mathematical Journal
publication date: 2003-05-19T00:00:00Z
review text: The paper deals with a system which is elliptic (in the Petrovskii sense) in a bounded domain and strongly degenerate at the inner point \(0\) of the domain. The aim of the paper is to consider a modified Dirichlet problem in the class of vector functions that unboundedly increase (in the absolute value) as \(x\to 0\). The modification means that in addition to a Dirichlet-type condition on the boundary, the principal term of the asymptotics of a solution at the point \(0\) is given. The existence and uniqueness of a solution of the problem considered in a weighted class of Hölder vector functions is proved.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1912595
zbMATH Keywords: degenerate elliptic systems
zbMATH Keywords: asymptotics of solutions
zbMATH Keywords: modified Dirichlet problem
reviewed by: G. Jaiani
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1912595