TY - JOUR
T1 - On time regularity of stochastic evolution equations with monotone coefficients
AU - Breit, Dominic
AU - Hofmanová, Martina
PY - 2016/1
Y1 - 2016/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84953836899&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2015.09.031
DO - 10.1016/j.crma.2015.09.031
M3 - Article
AN - SCOPUS:84953836899
VL - 354
SP - 33
EP - 37
JO - Comptes Rendus Mathématique
JF - Comptes Rendus Mathématique
SN - 1631-073X
IS - 1
ER -