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.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2102.12414
 Bibcode:
 2021arXiv210212414S
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability;
 35K55;
 35R60;
 60H15;
 35D99
 EPrint:
 27 pages, corrections in the title and in the abstract. arXiv admin note: substantial text overlap with arXiv:1908.11186