Capacity of rings and mappings generate embeddings of Sobolev spaces

TL;DR

This paper characterizes mappings that generate embeddings of Sobolev spaces using ring capacity inequalities and shows these mappings are Lipschitz in certain capacitory metrics.

Contribution

It introduces new characterizations of Sobolev space embeddings via ring capacity inequalities and establishes Lipschitz continuity in sub-hyperbolic capacitory metrics.

Findings

Mappings generating Sobolev embeddings satisfy ring capacity inequalities

Such mappings are Lipschitz in sub-hyperbolic capacitory metrics

Provides new insights into the structure of Sobolev space embeddings

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.