Fractional Sobolev Regularity for the Brouwer Degree

Camillo De Lellis, Dominik Inauen

We prove that if $\Omega \subset {\mathbb{R}}^n$ is a bounded open set and $n\alpha >{\dim }_b(\partial \Omega )=d$, then the Brouwer degree deg$(v,\Omega ,\cdot )$ of any Hölder function $v\in C^{0,α}\…