Symmetry of ground states of quasilinear elliptic equations

. We consider the problem of radial symmetry for non-negative continuously differentiable weak solutions of elliptic equations of the form (ProQuest: Formulae and/or non-USASCII text omitted; see image) under the ground state condition (ProQuest: Formulae and/or non-USASCII text omitted; see image)...

Full description

Saved in:
Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 148; no. 4; pp. 265 - 290
Main Authors SERRIN, J, HENGHUI ZOU
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.09.1999
Berlin Springer Nature B.V
New York, NY
Subjects
Exact sciences and technology
Mathematical methods in physics
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Studies
Symmetry
Laplace equations
Sufficient condition
Weak solution
Ground states
Elliptic equations
Online AccessGet full text

Cover

More Information
Summary:. We consider the problem of radial symmetry for non-negative continuously differentiable weak solutions of elliptic equations of the form (ProQuest: Formulae and/or non-USASCII text omitted; see image) under the ground state condition (ProQuest: Formulae and/or non-USASCII text omitted; see image) Using the well-known moving plane method of Alexandrov and Serrin, we show, under suitable conditions on A and f, that all ground states of (1) are radially symmetric about some origin O in (ProQuest: Formulae and/or non-USASCII text omitted; see image) . In particular, we obtain radial symmetry for compactly supported ground states and give sufficient conditions for the positivity of ground states in terms of the given operator A and the nonlinearity f.[PUBLICATION ABSTRACT]
ISSN:0003-9527
1432-0673
DOI:10.1007/s002050050162