On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs
Analysis of PDEs
2025-07-21 v2 Differential Geometry
Abstract
We study anisotropic geometric energy functionals defined on a class of k-dimensional surfaces in a Euclidean space. The classical notion of ellipticity, coming from Almgren, for such functionals is investigated. We prove a variant of a recent result of De Rosa, Lei, and Young and show that uniform ellipticity of an anisotropic energy functional with respect to real polyhedral chains implies uniform polyconvexity of the integrand.
Keywords
Cite
@article{arxiv.2501.12472,
title = {On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs},
author = {Maciej Lesniak},
journal= {arXiv preprint arXiv:2501.12472},
year = {2025}
}