Elliptic Problems with a Shift in Complete Scales of Sobolev-Type Spaces

Abstract

General boundary value problems with a shift for elliptic equations were first studied in [1]; such problems arise for instance by studying certain steady-state oscillations. They are natural generalization of the well-known Carleman boundary value problems for analytic functions. In this contribution we prove the isomorphism theorem for such problems (i.e. the solvability theorem in complete scales of Sobolev-type spaces). In the author’s previous paper [2] such theorem was obtained under additional assumption of normality of the boundary conditions. We consider also some applications of the isomorphism theorem, in particular, the local increasing of smoothness of generalized solutions and the existence and smoothness properties of the Green’s function of elliptic problem with a shift.