Boundary Layer Methods for Lipschitz Domains in Riemannian Manifolds

Abstract

We extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the Laplace equation and certain other constant coefficient elliptic partial differential equations on Lipschitz domains in Euclidean space. We treat the Laplace operator on Lipschitz domains in a manifold withC1metric tensor and study the Dirichlet, Neumann, and oblique derivative boundary problems.