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Recently, Giorgio Fusco and the author studied the system {\Delta}u - W_u (u)= 0 for a class of potentials that possess several global minima and areinvariant under a general finite reflection group, and established existence ofequivariant solutions connecting the minima in certain directions at infinity,together with an estimate. In this paper a new proof is given which, inparticular, avoids the introduction of a pointwise constraint in theminimization process.

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