Elliptic transmission problem in disjoint domains

摘要

In this paper, we investigate an elliptic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. A finite di.erence scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smo othness of the input data (up to a slowly increasing logarithmic factor of the mesh size), is obtained.