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A new proof for the existence of an equivariant entire solution connecting the minima of the potential for the system Δu - W_u (u) = 0

Recently, Giorgio Fusco and the author studied the system Δu - 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 the introduction of a pointwise constraint in the minimization process.

preprint2011arXivOpen access
Nicholas D. Alikakos
math.AP
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Nicholas D. Alikakos

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