Regularity and compactness for critical points of degenerate polyconvex energies

Fuente: arXiv
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Main Authors: Guerra, André, Tione, Riccardo
Format: Preprint
Published: 2024
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author Guerra, André
Tione, Riccardo
author_facet Guerra, André
Tione, Riccardo
contents We study Lipschitz critical points of the energy $\int_Ωg(\det D u) \, d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers in particular an open problem posed by Kirchheim, Müller and Šverák in 2003.
format Preprint
id arxiv_https___arxiv_org_abs_2401_16315
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Regularity and compactness for critical points of degenerate polyconvex energies
Guerra, André
Tione, Riccardo
Analysis of PDEs
We study Lipschitz critical points of the energy $\int_Ωg(\det D u) \, d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers in particular an open problem posed by Kirchheim, Müller and Šverák in 2003.
title Regularity and compactness for critical points of degenerate polyconvex energies
topic Analysis of PDEs
url https://arxiv.org/abs/2401.16315