3 papers
math.FA2025
The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms
Marcel Schmidt, Ian Zimmermann
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…
math.AP2024
A non-linear characterization of stochastic completeness of graphs
Marcel Schmidt, Ian Zimmermann
We study non-linear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion…
math.AP2021
Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source
Daniel Lenz, Marcel Schmidt, Ian Zimmermann
We give a sufficient condition for non-existence of global nonnegative mild solutions of the Cauchy problem for the semilinear heat equation in for $p \…