Regularity and compactness for critical points of degenerate polyconvex energies

2024/01/29 by Guerra, André, Tione, Riccardo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.16315

Abstract

We study Lipschitz critical points of the energy ∫_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.

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