Domination of nonlinear semigroups generated by regular, local Dirichlet forms

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Abstract

In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form E dominates the semigroup generated by another local functional F if, and only if, F is a specific zero order perturbation of E. On the way, we prove a nonlinear version of the Riesz–Markov representation theorem, we define an abstract boundary of a topological measure space, and apply the notion of nonlinear capacity. The main result helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.

Details

OriginalspracheEnglisch
Seiten (von - bis)163-188
Seitenumfang26
FachzeitschriftAnnali di matematica pura ed applicata : organo della Fondazione Annali di Matematica Pura ed Appliecata
Jahrgang204
Ausgabenummer1
PublikationsstatusVeröffentlicht - Juli 2024
Peer-Review-StatusJa

Externe IDs

ORCID /0000-0002-6854-0586/work/162841780
Scopus 85197458599