English

Sobolev embeddings with weights in complete riemannian manifolds

Analysis of PDEs 2019-06-02 v2

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.

Keywords

Cite

@article{arxiv.1902.08613,
  title  = {Sobolev embeddings with weights in complete riemannian manifolds},
  author = {Eric Amar},
  journal= {arXiv preprint arXiv:1902.08613},
  year   = {2019}
}

Comments

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