Sobolev homeomorphisms with gradients of low rank via laminates

Daniel Faraco, Carlos Mora-Corral, Marcos Oliva

Let $\Omega \subset {\mathbb{R}}^n$ be a bounded open set. Given $2\le m\le n$, we construct a convex function $\varphi :\Omega \to \mathbb{R}$ whose gradient $f=\nabla \varphi$ is a Hölder continuous h…