Abstract
We consider the system Δu − W u (u) = 0, where \({u : \mathbb{R}^n \to \mathbb{R}^n}\) , for a class of potentials \({W : \mathbb{R}^n \to \mathbb{R}}\) that possess several global minima and are invariant under a general finite reflection group G. We establish existence of nontrivial G-equivariant entire solutions connecting the global minima of W along certain directions at infinity.
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Communicated by D. Kinderlehrer
Nicholas D. Alikakos was supported by Kapodistrias grant No. 15/4/5622 at the University of Athens.
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Alikakos, N.D., Fusco, G. Entire Solutions to Equivariant Elliptic Systems with Variational Structure. Arch Rational Mech Anal 202, 567–597 (2011). https://doi.org/10.1007/s00205-011-0441-z
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DOI: https://doi.org/10.1007/s00205-011-0441-z