On compactly-supported approximation of differential forms in weighted Sobolev-type spaces (Q1335961)

Let \(W_ p^ k (M,\sigma)\) be the space of measurable differential forms of degree \(k\) on a Riemannian manifold \(M\) with the norm \[ \|\omega\|= \Biggl\{ \int_ M \bigl[ \sigma_ k^ p (x)| \omega(x)|^ p+ \sigma_{k+1}^ p (x)| d\omega(x)|^ p \bigr]dx \Biggr\}^{1\over p}, \] where \(\sigma_ k\) and \(\sigma_{k+1}\) are weight functions, \(1\leq p<\infty\). And let \(V_ p^ k (M,\sigma)\) be the subspace of smooth compactly-supported forms. Necessary and sufficient conditions are obtained for a form belonging to \(V_ p^ k (M,\sigma)\), when \(M\) is a wrapped cylinder over a compact manifold.