On the Smoothness of Solutions to Elliptic Equations in Domains with Hölder Boundary

Abstract

The dependence of the smoothness of variational solutions to the first boundary value problems for second order elliptic operators is studied. The results use Sobolev–Slobodetskii and Nikolskii–Besov spaces and their properties. Methods are based on the real interpolation technique and on generalization of the Savaré–Nirenberg difference quotient technique.