Sobolev inequalities for nonlinear Dirichlet forms

TL;DR

This paper establishes an equivalence between Sobolev inequalities and isocapacitary inequalities within the framework of nonlinear Dirichlet forms, linking functional inequalities with capacity concepts.

Contribution

It introduces a novel equivalence connecting Sobolev and isocapacitary inequalities for nonlinear Dirichlet forms, expanding the theoretical understanding of these inequalities.

Findings

Proves the equivalence between Sobolev and isocapacitary inequalities.

Applies to a broad class of nonlinear Dirichlet forms.

Enhances the theoretical framework linking inequalities and capacities.

Abstract

In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated capacities.