A Priori Estimates for Solutions to
Elliptic Equations on Non-Smooth Domains

Abstract

It is proved that elliptic boundary value problems have a smoothing property in Lebesgue spaces provided the underlying space of weak solutions admits a Sobolev type inequality. The results apply to all standard boundary conditions and a wide range of non-smooth domains, even if the classical estimates fail. The dependence on the data is explicit. In particular, this provides good control over the domain dependence, which is important for applications involving varying domains