Domination of nonlinear semigroups generated by regular, local Dirichlet forms

Abstract: In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. We show that the semigroup of a local Dirichlet form (\mathcal{E}) dominates the semigroup generated by another functional (\mathcal{F}) if, and only if, (\mathcal{F}) is a specific zero order perturbation of (\mathcal{E}). This helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.