Minimality of polytopes in a nonlocal anisotropic isoperimetric problem

Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu

发表信息：: Nonlinear Analysis 205 (2021) 112223
DOI：: 10.1016/j.na.2020.112223

英文摘要：

We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the anisotropic perimeter has certain symmetry properties, then it is the unique global minimizer of the total energy. In dimension two this applies to convex polygons which are reflection symmetric with respect to the bisectors of the angles. We further prove a rigidity result for the structure of (local) minimizers in two dimensions.

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