Elliptic transmission problem in disjoint domains

Abstract

In this paper, we investigate an elliptic transmission problem indisjoint domains. A priori estimate for its weak solution inappropriate Sobolev-like space is proved. A finite differencescheme approximating this problem is proposed and analyzed. Anestimate of the convergence rate, compatible with the smoothnessof the input data (up to a slowly increasing logarithmic factor ofthe mesh size), is obtained.