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

TL;DR

This paper studies the temporal regularity of strong solutions to stochastic p-Laplace systems, establishing fractional differentiability properties in specialized function spaces under stochastic forcing.

Contribution

It proves 1/2 time differentiability of solutions and their nonlinear gradients in advanced function spaces for stochastic p-Laplace systems, extending regularity theory.

Findings

Solutions are 1/2 time differentiable in Besov-Orlicz spaces.

Nonlinear gradients exhibit 1/2 time differentiability in Nikolskii spaces.

Results apply to degenerate stochastic p-Laplace systems with multiplicative noise.

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.