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Sobolev embeddings with weights in complete riemannian manifolds · arXivDesk

1902.08613Feb 21, 2019We 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

Sobolev embeddings with weights in complete riemannian manifolds

Eric Amar

Analysis of PDEs

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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.

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We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold. We also get general Gaffney's inequality with weights.

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The paper addresses: Sobolev embeddings with weights in complete riemannian manifolds.
We prove Sobolev embedding Theorems with weights for vector bundles in a complete riemannian manifold.

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Author comment: 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