Year: 2026
Type: preprint
Abstract: We prove an arbitrary-dimensional halfspace theorem for global minimizers of a smooth uniformly elliptic anisotropic perimeter: if the nonempty boundary of a minimizing set is contained in a halfspace, then the set itself is a halfspace. No evenness of the integrand or regularity of the minimizing boundary is assumed. The proof combines wall contact with a plane-peeling argument for the complementary phase defect and a simultaneous second blow-down. We also give a direct, self-contained exterior-barrier proof of the two-dimensional stationary anisotropic statement. Its rigidity conclusion is already covered by Bergner's earlier halfspace theorem; the proof is retained because it works directly with the anisotropic Euler-Lagrange operator.
Source: arXiv (Cornell University)
Author: Yang, Yang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208723201