Nonlinear Beurling-Deny criteria

TL;DR

This paper introduces a symmetric contraction property for functionals that characterizes Dirichlet forms in both linear and non-linear cases, offering new insights into existing criteria.

Contribution

It presents a simple symmetric contraction property that characterizes Dirichlet forms non-linearly, extending previous linear characterizations and providing new perspectives on established criteria.

Findings

The property characterizes Dirichlet forms in the non-linear setting.

It offers a unified view of linear and non-linear Dirichlet forms.

Provides new insights into Cipriani/Grillo and Brigati/Hartarsky criteria.

Abstract

This short note introduces a simple symmetric contraction property for functionals. This property clearly characterizes Dirichlet forms in the linear case. We show that it also characterizes Dirichlet forms in the non-linear case. Furthermore, we use this property to gain a new perspective on criteria of Cipriani / Grillo as well as Brigati / Hartarsky.