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<p>We study anisotropic geometric energy functionals defined on a class of <i>k</i>-dimensional surfaces in a&#xa0;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 <i>uniform</i> ellipticity of an anisotropic energy functional with respect to real polyhedral chains implies <i>uniform</i> polyconvexity of the integrand.</p>

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On polyconvexity and almgren uniform ellipticity with respect to polyhedral test pairs

  • 期刊论文

  • 发表日期：

    2025年7月27日

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  • Maciej Lesniak

摘要

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.