Potential theory on lipschitz domains in riemannian manifolds: hölder continuous metric tensors

Abstract

In our papers [MT], [MT2], [MT3], and [MMT], we have developed the method of layer potentials as a tool to treat boundary problems for the Laplace operator and related operators on Lipschitz domains in Riemannian manifolds, extending work done on Lipschitz domains in Euclidean space with its standard flat metric, beginning with the papers of [FJR], [Ve], and [DK]. We worked under the hypothesis that the metric tensor was at least Lipschitz. Here our goal is to relax this regularity hypothesis and work with metric tensors that are merely Holder continuous.