preprint
Inserted: 30 jan 2024
Year: 2024
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.