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

Abstract

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 equations with $L^1$-initial data and study existence and uniqueness of solutions in this framework.

27 pages, corrections in the title and in the abstract. arXiv admin note: substantial text overlap with arXiv:1908.11186