The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms

TL;DR

This paper develops the theory of extended Dirichlet spaces for nonlinear Dirichlet forms, introducing criticality and subcriticality concepts, and laying foundational aspects of potential theory under mild conditions.

Contribution

It is the first to establish the existence of extended Dirichlet spaces for nonlinear forms and to characterize criticality and transience in this context.

Findings

Existence of extended Dirichlet space for nonlinear forms

Characterization of criticality and subcriticality

Foundations of potential theory for nonlinear Dirichlet forms

Abstract

In this paper we establish the existence of the extended Dirichlet space for nonlinear Dirichlet forms under mild conditions. We employ it to introduce and characterize criticality (recurrence) and subcriticality (transience) and establish basics of a potential theory.