Open AccessA study on stochastic maximal regularity for rough time-dependent problems
Author(s) -
P Govindaraju,
Sasikala,
Mohamed Ali A
Publication year - 2021
Publication title -
journal of computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-8686
DOI - 10.26524/cm92
Subject(s) - mathematics , divergence (linguistics) , semigroup , brownian motion , order (exchange) , space (punctuation) , mathematical analysis , random variable , statistics , computer science , philosophy , linguistics , finance , economics , operating system
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only progressively measurable in the time variable. For 2m-th order systems with VMO regularity in space, we obtain Lp(Lq) estimates for all p > 2 and q ≥ 2, leading to optimal space-time regularity results. For second order systems with continuous coefficients in space, we also include a first order linear term, under a stochastic parabolicity condition, and obtain Lp(Lp) estimates together with optimal space-time regularity. For linear second order equations in divergence form with random coefficients that are merely measurable in both space and time, we obtain estimates in the tent spaces Tp,2 of Coifman-Meyer-Stein. This is done in the deterministic case under no extra assumption, and in the stochastic case under the assumption that the coefficients are divergence free.