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

@article{Sapountzoglou2021WellposednessOR,
  title={Well-posedness of renormalized solutions for a stochastic p -Laplace equation with L^1 -initial data},
  author={Niklas Sapountzoglou and Aleksandra Zimmermann},
  journal={Discrete \& Continuous Dynamical Systems - A},
  year={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 is given by a stochastic integral in the sense of Ito. The technical difficulties arise from the merely integrable random initial data $u_0$ under consideration. Due to the poor regularity of the initial data, estimates in $W^{1,p}_0(D)$ are available with respect to truncations of the solution… 

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