Elliptic equations strongly degenerate at a point

In this paper we will mainly propose some problems for a class of degenerate elliptic equations, either linear or nonlinear. We will study some special cases of these problems and reveal some phenomena which may not have been noticed previously. Our problems originated from the self-similar solution...

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Published inNonlinear analysis Vol. 65; no. 8; pp. 1624 - 1632
Main Authors Weiyue, Ding, Yongqiang, Zhao
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 15.10.2006
Elsevier
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Elliptic equation
Mathematical model
Nonlinear analysis
Degenerate equation
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Summary:In this paper we will mainly propose some problems for a class of degenerate elliptic equations, either linear or nonlinear. We will study some special cases of these problems and reveal some phenomena which may not have been noticed previously. Our problems originated from the self-similar solutions of the heat flow of harmonic maps. We will prove that the self-similar solutions or the so-called quasi-harmonic spheres are discontinuous at infinity for the equivariant case. In other words, the equivariant quasi-harmonic spheres are not continuous images of topological spheres.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.10.037