A basilar property and a useful tool in the theory of Sobolev spaces is density smooth compactly supported functions space $W^{k,p}(\R^n)$ (i.e. with weak derivatives orders $0$ to $k$ $L^p$). On Riemannian manifolds, it well known that same remains valid under suitable geometric assumptions. However, on complete non-compact manifold can fail be true general, as we prove this paper. This settle...
