On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs
arXiv:2501.12472 · doi:10.1007/s00229-025-01649-4
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.