Minimizing under relaxed symmetry constraints: Triple and N-junctions

2021/06/17 by Giorgio Fusco, Fusco, Giorgio · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Analytic and geometric function theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2106.09448

Abstract

We consider a nonnegative potential W:ℝ²→ℝ invariant under the action of the rotation group C_N of the regular polygon with N sides, N≥ 3. We assume that W has N nondegenerate zeros and prove the existence of a N-junction solution to the vector Allen-Cahn equation. The proof is variational and is based on sharp lower and upper bounds for the energy and on a new pointwise estimate for vector minimizers.

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