Sobolev solutions of parabolic equation in a complete riemannian manifold
arXiv:1812.04411
Abstract
We study Sobolev estimates for the solutions of parabolic equations acting on a vector bundle, in a complete, compact or non compact, riemannian manifold The idea is to introduce geometric weights on We get global Sobolev estimates with these weights. As applications, we find and improve "classical results", i.e. results without weights, by use of a Theorem by Hebey and Herzlich. As an example we get Sobolev estimates for the solutions of the heat equation on -forms when the manifold has "weak bounded geometry " of order .
An global implicit assumption is made explicit. Some typos are corrected. The results remaind unchanged