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

We consider a $ p $-Laplace evolution problem with stochastic forcing on bounded domain D\subset\mathbb{R}^d homogeneous Dirichlet boundary conditions for 1<p<\infty $. The additive noise term is given by integral in the sense of Itô. technical difficulties arise from merely integrable random initial data u_0 under consideration. Due to poor regularity data, estimates W^{1,p}_0(D) are available respect truncations solution only and therefore well-posedness results have be formulated generalized solutions. extend notion renormalized this type SPDEs, show setting study Markov properties