The structure of fractional spaces generated by a two-dimensional elliptic differential operator and its applications

Abstract

We consider the two-dimensional differential operator [InlineEquation not available: see fulltext.] defined on functions on the half-plane [InlineEquation not available: see fulltext.] with the boundary conditions [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], are continuously differentiable and satisfy the uniform ellipticity condition [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]. The structure of the fractional spaces [InlineEquation not available: see fulltext.] generated by the operator A is investigated. The positivity of A in Hölder spaces is established. In applications, theorems on well-posedness in a Hölder space of elliptic problems are obtained.

MSC: 35J25, 47E05, 34B27.