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

Speaker(s)

Maciej Leśniak

Language of the talk

English

Date

May 7, 2025, 12:30 p.m.

Room

room 3170

Seminar

Seminarium Zakładu Równań i Analizy

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The ellipticity of an anisotropic energy functional is a property that
ensures a flat k-cube is the unique minimizer of the functional among all
competitors with the same (k-1)-dimensional boundary as the cube. There is
a strong relation between the ellipticity of a functional and the
(poly)convexity of its integrand, which has been investigated by
Burago-Ivanov, and recently by De Rosa, Lei, and Young. In this talk, we
extend a recent result by De Rosa, Lei, and Young and show that the uniform
ellipticity of an anisotropic energy functional with respect to polyhedral
chains implies the uniform polyconvexity of the integrand.
 

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