Capacity of rings and mappings generate embeddings of Sobolev spaces

Abstract

In this paper we give characterizations of mappings generate embeddings of Sobolev spaces in the terms of ring capacity inequalities. In addition we prove that such mappings are Lipschitz mappings in the sub-hyperbolic type capacitory metrics.

arXiv comment17 pages. arXiv admin note: text overlap with arXiv:2110.09261