Linear Elliptic Boundary Value Problems with Non - Smooth Data: Normal Solvability on Sobolev - Campanato Spaces

Abstract

In this paper linear elliptic boundary value problems of second order with non – smooth data (L∞ – coeffcients, Lipschitz domains, regular sets, non – Chomogeneous mixed boundary conditions) are considered. It is shown that such boundary value problems generate Fredholm operators between appropriate Sobolev – Campanato spaces, that the weak solutions are Hölder continuous up to the boundary and that they depend smoothly (in the sense of a Hölder norm) on the coefficients and on the right – hand sides of the equations and boundary conditions.