A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System Delta u - W sub( )uu) = 0

Recently, Giorgio Fusco and the author in [2] studied the system Delta u - W sub( )uu) = 0 for a class of potentials that possess several global minima and are invariant under a general finite reflection group, and established existence of equivariant solutions connecting the minima in certain direc...

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Bibliographic Details
Published in:	Communications in partial differential equations Vol. 37; no. 12; pp. 2093 - 2115
Main Author:	Alikakos, Nicholas D
Format:	Journal Article
Language:	English
Published:	01-01-2012
Subjects:	Infinity Invariants Joining Mathematical analysis Minima Optimization Proving Reflection
Online Access:	Get full text
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Summary:	Recently, Giorgio Fusco and the author in [2] studied the system Delta u - W sub( )uu) = 0 for a class of potentials that possess several global minima and are invariant under a general finite reflection group, and established existence of equivariant solutions connecting the minima in certain directions at infinity, together with an estimate. In this paper a new proof is given which, in particular, avoids both the introduction of a pointwise constraint in the minimization process and the equivariant extensions of the various test functions.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 content type line 23 ObjectType-Feature-1
ISSN:	0360-5302 1532-4133
DOI:	10.1080/03605302.2012.721851