• Corpus ID: 232035606

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

@inproceedings{Sapountzoglou2021RenormalizedSF,
title={Renormalized solutions for stochastic \$p\$-Laplace equations with \$L^1\$-initial data: The multiplicative case},
author={Niklas Sapountzoglou and Aleksandra Zimmermann},
year={2021}
}
• Published 24 February 2021
• Mathematics
We consider a p-Laplace evolution problem with multiplicative noise on a bounded domain D ⊂ R with homogeneous Dirichlet boundary conditions for 1 < p < ∞. 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 pLaplace equations with L1-initial data and study existence and uniqueness of solutions in this framework.

## References

SHOWING 1-10 OF 29 REFERENCES

### Well-posedness of renormalized solutions for a stochastic p -Laplace equation with L^1 -initial data

• Mathematics
Discrete & Continuous Dynamical Systems - A
• 2021
We consider a $p$-Laplace evolution problem with stochastic forcing on a bounded domain $D\subset\mathbb{R}^d$ with homogeneous Dirichlet boundary conditions for $1<p<\infty$. The additive noise term

### Well-posedness for a pseudomonotone evolution problem with multiplicative noise

• Mathematics
Journal of Evolution Equations
• 2018
Our aim is the study of well-posedness for the stochastic evolution equation \begin{aligned} \mathrm{d}u -\mathrm {div}\,(|\nabla u|^{p-2}\nabla u +F(u)) \,\mathrm{d} t = H(u) \,\mathrm{d}W,

### Stochastic Partial Differential Equations: An Introduction

• Mathematics
• 2015
Motivation, Aims and Examples.- Stochastic Integral in Hilbert Spaces.- SDEs in Finite Dimensions.- SDEs in Infinite Dimensions and Applications to SPDEs.- SPDEs with Locally Monotone Coefficients.-

### Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness

• Mathematics
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
• 1997
In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problem where the data f and u0 belong to L1(Ω × (0, T)) and L1 (Ω), and where the function a:(0, T) ×

### On the Cauchy problem for Boltzmann equations: global existence and weak stability

• Mathematics
• 1989
We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge