Nonlinear Beurling-Deny criteria

2025/02/06 by Simon Puchert, Puchert, Simon · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.03691

openalex publication_date 2025/02/06 · openalex created_date 2025/02/08 · openalex updated_date 2026/07/28

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.

Cited by

• Nonlinear resistance forms

Related

• Computations and global properties for traces of Bessel's Dirichlet form
• Beurling-Deny formula for Sobolev-Bregman forms
• Nonlinear Dirichlet forms, energy spaces, and calculus rules
• (Weak) Hardy and Poincaré inequalities and criticality theory
• The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms