Regular elliptic boundary-value problems in the extended Sobolev scale

Abstract

We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean domain with infinitely smooth boundary. We prove that the operator of the problem is bounded and Fredholm in appropriate pairs of H\"ormander inner product spaces. They are parametrized with the help of an arbitrary radial function RO-varying at infinity and form the extended Sobolev scale. We establish a priori estimates for solutions to the problem and investigate their local regularity on this scale. We find new sufficient conditions for generalized partial derivatives of the solutions to be continuous.