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arXiv · 2110.00951

H\"older estimates for solutions of parabolic SPDEs

Sergey Kuksin·Nikolai Nadirashvili·Andrey Piatnitski
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Abstract

This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of $\mathbb R^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large $p$. We prove that the solutions are H\"older-continuous functions almost surely (a.s.) and that the respective H\"older norms have finite momenta of any order.

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Sergey Kuksin, Nikolai Nadirashvili, Andrey Piatnitski. 2021-10-03. H\"older estimates for solutions of parabolic SPDEs. https://arxiv.org/abs/2110.00951

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