# The stochastic $p$-Laplace equation on $\mathbb{R}^d$

@inproceedings{Schmitz2020TheS, title={The stochastic \$p\$-Laplace equation on \$\mathbb\{R\}^d\$}, author={Kerstin Schmitz and Aleksandra Zimmermann}, year={2020} }

We show well-posedness of the p -Laplace evolution equation on R d with square integrable random initial data for arbitrary 1 < p < ∞ and arbitrary space dimension d ∈ N . The noise term on the right-hand side of the equation may be additive or multiplicative. Due to a lack of coercivity of the p -Laplace operator in the whole space, the possibility to apply well-known existence and uniqueness theorems in the classical functional setting is limited to certain values of 1 < p < ∞ and also…

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