A right inverse of the divergence for planar Hölder-$\alpha$ domains

Ricardo G. Durán, Fernando López García

If $\Omega \subset {\mathbb{R}}^n$ is a bounded domain, the existence of solutions $\mathbf{u}\in H_0^1(\Omega {)}^n$ of $div\mathbf{u}=f$ for $f\in L^2(\Omega )$ with vanishing mean value, is a basic result in t…