Weak stability by noise for approximations of doubly nonlinear evolution equations
Probability
2025-07-24 v1 Analysis of PDEs
Abstract
Doubly nonlinear stochastic evolution equations are considered. Upon assuming the additive noise to be rough enough, we prove the existence of probabilistically weak solutions of Friedrichs type and study their uniqueness in law. This entails stability for approximations of stochastic doubly nonlinear equations in a weak probabilistic sense. Such effect is a genuinely stochastic, as doubly nonlinear equations are not even expected to exhibit uniqueness in the deterministic case.
Cite
@article{arxiv.2507.17331,
title = {Weak stability by noise for approximations of doubly nonlinear evolution equations},
author = {Carlo Orrieri and Luca Scarpa and Ulisse Stefanelli},
journal= {arXiv preprint arXiv:2507.17331},
year = {2025}
}