Layer Potential Analysis for Pseudodifferential Matrix Operators in Lipschitz Domains on Compact Riemannian Manifolds: Applications to Pseudodifferential Brinkman Operators

Abstract

The goal of this paper was to develop a potential analysis for a certain type of pseudodifferential matrix operators on Lipschitz domains in compact Riemannian manifolds and apply this analysis to treat boundary value problems for general Brinkman operators on such Lipschitz domains and boundary data in various Sobolev spaces.