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

Niklas Sapountzoglou; Aleksandra Zimmermann

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

Analysis of PDEs 2021-03-02 v2 Probability

Authors: Niklas Sapountzoglou , Aleksandra Zimmermann

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.

Keywords

regularity for elliptic equations stochastic partial differential equations partial differential equations

Cite

@article{arxiv.2102.12414,
  title  = {Renormalized solutions for stochastic $p$-Laplace equations with $L^1$-initial data: The multiplicative case},
  author = {Niklas Sapountzoglou and Aleksandra Zimmermann},
  journal= {arXiv preprint arXiv:2102.12414},
  year   = {2021}
}

Comments

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

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

Abstract

Keywords

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