Published Paper

Inserted: 30 jan 2024
Last Updated: 4 nov 2024

Journal: Arch. Rational Mech. Anal.
Year: 2024
Doi: https://doi.org/10.1007/s00205-024-02055-y

Abstract:

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.