Sobolev solutions of parabolic equation in a complete Riemannian manifold
Eric Amar

Abstract. We study Sobolev estimates for the solutions of parabolic equations acting on a vector bundle, in a complete Riemannian manifold M. The idea is to introduce geometric weights on M. We get global Sobolev estimates with these weights. As applications, we find and improve ``classical results'', i.e. results without weights. As an example we get Sobolev estimates for the solutions of the heat equation on p-forms when the manifold has``weak bounded geometry'' of order 1

Rend. Mat. Appl. (7) 41 (2020) 117-154; pdf