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arXiv · 2501.12472

On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs

Maciej Lesniak
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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.

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Maciej Lesniak. 2025-01-21. On Polyconvexity and Almgren Uniform Ellipticity With Respect to Polyhedral Test Pairs. https://doi.org/10.1007/s00229-025-01649-4

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