Rigidity of critical points of degenerate polyconvex energies

09:30-10:30 Thursday, 3 April 2025Auditorium, Rectorate

Abstract

This talk concerns critical points $u$ of polyconvex energies of the form $f(X) = g(det(X))$, where $g$ is (uniformly) convex. It is not hard to see that, if $u$ is smooth, then $\det(Du)$ is constant. I will show that the same result holds for Lipschitz critical points $u$ in the plane. If time allows, I will also discuss how to obtain rigidity for approximate solutions. This is a joint work with A. Guerra.