NEUMANN-TRANSMISSION PROBLEMS FOR PSEUDODIFFERENTIAL BRINKMAN OPERATORS ON LIPSCHITZ DOMAINS IN COMPACT RIEMANNIAN MANIFOLDS

摘要

The aim of this paper is twofold. On the one hand we construct Neumann-transmission kernels for pseudodifferential Brinkman operators. They are used to provide simple representations of the solution to some transmission problems for the pseudodifferential Brinkman operator. On the other hand, we show the well-posedness of a Neumann-transmission problem for two pseudodifferential Brinkman operators on adjacent Lipschitz domains in a compact Riemannian manifold, with boundary data in some L~p, Sobolev or Besov spaces. We rely on the layer potential theory in order to obtain an explicit representation of the solution to this problem. Compactness and invertibility results of associated layer potential operators on L~p, Sobolev and Besov spaces are also presented.