On temporal regularity of strong solutions to stochastic \(p\)-Laplace systems. (English) Zbl 1522.35131
Summary: In this article we investigate the temporal regularity of strong solutions to the stochastic \(p\)-Laplace system in the degenerate setting, \(p \in [2,\infty)\), driven by a multiplicative nonlinear stochastic forcing. We establish 1/2 time differentiability in an exponential Besov-Orlicz space for the solution process \(u\). Furthermore, we prove 1/2 time differentiability of the nonlinear gradient \(V(\nabla u)\) in a Nikolskii space.
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D35 | Strong solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K58 | Semilinear parabolic equations |
| 35K65 | Degenerate parabolic equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
Keywords:
SPDEs; nonlinear Laplace-type systems; strong solutions; regularity; stochastic \(p\)-heat equationReferences:
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