Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem

We continue a program to develop layer potential techniques for PDE on Lipschitz domains in Riemannian manifolds. Building on L-p and Hardy space estimates established in previous papers, here we establish Sobolev and Besov space estimates on solutions to the Dirichlet and Neumann problems for the Laplace operator plus a potential, on a Lipschitz domain in a Riemannian manifold with a metric tensor smooth of class C1 + gamma, for some gamma > 0. We treat the inhomogeneous problem and extend it to the setting of manifolds results obtained for the constant-coefficient Laplace operator on a Lipschitz domain in Euclidean space, with the Dirichlet boundary condition, by D. Jerison and C. Kenig. (C) 2000 Academic Press.