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.
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