Boundary value problems on non-Lipschitz uniform domains: Stability, compactness and the existence of optimal shapes

Michael Hinz, Anna Rozanova-Pierrat, Alexander Teplyaev

We study boundary value problems for bounded uniform domains in ${\mathbb{R}}^n$, $n\ge 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincaré inequalities with…