Normal solvability of elliptic boundary value problems on asymptotically flat manifolds

Abstract

Normal solvability is shown for a class of boundary value problems on Riemannian manifolds with noncompact boundary using a concept of weighted pseudodifferential operators and weighted Sobolev spaces together with Lopatinski-Shapiro type boundary conditions. An essential step is to show that the standard normal derivative defined in terms of the Riemannian metric is in fact a weighted pseudodifferential operator of the considered class provided the metric is compatible with the symbols.