Sobolev embeddings with weights in complete riemannian manifolds

Abstract

We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights. As a consequence, under a "weak bounded geometry" hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete riemannian manifold. We also improve known results on Gaffney's inequality in a complete riemannian manifold.

We introduce the notion of "weak bounded geometry" which allows us to improve clearly known results for Sobolev embeddings or Gaffney's inequality in complete non-compact riemannian manifolds. arXiv admin note: text overlap with arXiv:1812.04411