On temporal regularity for strong solutions to stochastic $p$-Laplace systems

Abstract

In this article we investigate the temporal regularity of strong solutions to the stochastic $p$-\com{L}aplace system in the degenerate setting, $p\in [2,\infty )$, driven by a multiplicative nonlinear stochastic forcing. We establish $1/2$ time differentiability in an expontential Besov-Orlicz space for the solution process $u$. Furthermore, we prove $1/2$ time differentiability of the nonlinear gradient $|\nabla u{|}^{\frac{p-2}{2}}\nabla u$ in a Nikolskii space.

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