Renormalized solutions for stochastic $p$-Laplace equation with $L^1$-initial data: The multiplicative case

Niklas Sapountzoglou, Aleksandra Zimmermann

Published 2021-02-24Version 1

We consider a $p$-Laplace evolution problem with multiplicative noise on a bounded domain $D \subset \mathbb{R}^d$ with homogeneous Dirichlet boundary conditions for $1<p< \infty$. The random initial data is merely integrable. Consequently, the key estimates are available with respect to truncations of the solution. We introduce the notion of renormalized solutions for multiplicative stochastic $p$-Laplace equation with $L^1$ initial data and study existence and uniqueness of solutions in this framework.