Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property

2014/03/06 by Sourdis, Christos
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.1538

Abstract

We prove a theorem for the growth of the energy of bounded, globally minimizing solutions to a class of semilinear elliptic systems of the form Δu=∇ W(u), x∈ ℝⁿ, n≥ 2, with W:ℝ^m→ ℝ, m≥ 1, nonnegative and vanishing at exactly one point (at least in the closure of the image of the considered solution u). As an application, we can prove a Liouville type theorem under various assumptions.

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