Given an elliptic integrand of class C2,α, we prove that finite unions of disjoint open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all sets with finite perimeter and reduced boundary almost equal to its closure.
Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets
De Rosa, Antonio;
2020
Abstract
Given an elliptic integrand of class C2,α, we prove that finite unions of disjoint open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all sets with finite perimeter and reduced boundary almost equal to its closure.
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