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

作者：Alikakos Nicholas D^*

来源：Communications in Partial Differential Equations, 2012, 37(12): 2093-2115.

DOI：10.1080/03605302.2012.721851

• Elliptic systems
• Phase translations
• Reflection group
• Variational calculus

Recently, Giorgio Fusco and the author in [2] studied the system Delta u - W-u(u) = 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.

• 出版日期2012