ON THE REGULARITY UP TO THE BOUNDARY OF SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS

Abstract

We consider the regularity up to the boundary of solutions of those elliptic boundary value problems that can be treated by the non-variational theory developed by Schechter and others. The usual method of differential quotients is replaced by a method of Schappel [5] which is based on the properties of a Laplace-type operator 1-∇2. In this paper the results of Schappel, which are given for boundary value problems in variational form, are extended to the non-variational case. We make important use of fractional order Sobolev spaces on the boundary and trace theorems.