An elliptic boundary problem for a system involving a discontinuous weight

Abstract

 In a recent paper, Agranovich, Denk and Faierman dealt with a priori estimates, completeness, Abel-Lidskii summability, and eigenvalue asymptotics for scalar elliptic boundary eigenvalue problems involving discontinuous weights. Here we extend these results to the matrix valued case with a diagonal discontinuous weight matrix. The given region is subdivided into subregions on which the weights are continuous. Whereas in the scalar case the usual ellipticity conditions suffice to obtain a priori estimates, a counterexample shows that here transmission conditions at the boundaries of the subregions are also needed.