On some equivalent norms in Sobolev spaces on bounded domains and on the boundaries

TL;DR

This paper investigates the equivalence of various norms in Sobolev spaces defined on bounded domains and their boundaries, providing insights into their mathematical relationships and potential applications.

Contribution

It establishes conditions under which certain Sobolev norms are equivalent on bounded domains and their boundaries, advancing theoretical understanding.

Findings

Identifies specific norm equivalences in Sobolev spaces

Provides criteria for norm equivalence on domains and boundaries

Enhances mathematical tools for analysis in Sobolev spaces

Abstract

We consider the equivalence of some norms in Sobolev spaces on bounded domains of the d-dimensional real Euclidean space and also in Sobolev spaces on the boundaries of those domains.