English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We report on a time regularity result for stochastic evolutionary PDEs withmonotone coefficients. If the diffusion coefficient is bounded in time withoutadditional space regularity we obtain a fractional Sobolev type time regularityof order up to $\tfrac{1}{2}$ for a certain functional $ G( u )$ of thesolution. Namely, $ G( u )=\nabla u $ in the case of the heat equation and $G(u )=|\nabla u |^{\frac{p-2}{2}}\nabla u $ for the $p$-Laplacian. The motivationis twofold. On the one hand, it turns out that this is the natural timeregularity result that allows to establish the optimal rates of convergence fornumerical schemes based on a time discretization. On the other hand, in thelinear case, i.e. where the solution is given by a stochastic convolution, ourresult complements the known stochastic maximal space-time regularity resultsfor the borderline case not covered by other methods.

On time regularity of stochastic evolution equations with monotone coefficients