Calculus of Variations and Geometric Measure Theory

A. Guerra - R. Tione

Regularity and compactness for critical points of degenerate polyconvex energies

created by tione on 30 Jan 2024



Inserted: 30 jan 2024

Year: 2024

ArXiv: 2401.16315 PDF


We study Lipschitz critical points of the energy $\int_\Omega g(\det D u) \, d x$ 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, M\"uller and \v{S}ver\'ak in 2003.