On time regularity of stochastic evolution equations with monotone coefficients

Dominic Breit, Martina Hofmanová

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Abstract

We report on a time regularity result for stochastic evolutionary PDEs with monotone coefficients. If the diffusion coefficient is bounded in time without additional space regularity, we obtain a fractional Sobolev-type time regularity of order up to 12 for a certain functional G(u) of the solution. Namely, G(u) = ∇. u in the case of the heat equation and G(u)=|∇u|p-22∇u for the p-Laplacian. The motivation is twofold. On the one hand, it turns out that this is the natural time regularity result that allows us to establish the optimal rates of convergence for numerical schemes based on a time discretization. On the other hand, in the linear case, i.e. when the solution is given by a stochastic convolution, our result complements the known stochastic maximal space-time regularity results for the borderline case not covered by other methods.

Original languageEnglish
Pages (from-to)33-37
Number of pages5
JournalComptes Rendus Mathématique
Volume354
Issue number1
DOIs
Publication statusPublished - Jan 2016

ASJC Scopus subject areas

  • Mathematics(all)

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