Fractional power approach for the study of elliptic second order boundary value problems with variable operator coefficients in Hölder spaces

Abstract

In this paper we study an abstract second order differential equation of elliptic type with variable operator coefficients and general Robin boundary conditions, in the framework of Hölder spaces. Existence and regularity results are obtained under the Labbas-Terreni assumption. We use, in particular, the semigroups the ory and the real interpolatin spaces. This work is naturally the continuation of the ones studied by R. Haoua [13] in the UMD spaces and homogenous cases.