STOCHASTIC MAXIMAL Lp-REGULARITY

• 成果类型: Article
• 署名作者: van Neerven, Jan; Veraar, Mark; Weis, Lutz
• 署名单位: Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP626
• 发表日期: 2012
• 页码: 788-812
• 关键词: partial-differential-equations; h-infinity-calculus; elliptic-operators; THEOREMS

摘要

In this article we prove a maximal L-p-regularity result for stochastic convolutions, which extends Krylov's basic mixed L-p(L-q)-inequality for the Laplace operator on R-d to large classes of elliptic operators, both on R-d and on bounded domains in R-d with various boundary conditions. Our method of proof is based on McIntosh's H-infinity-functional calculus, R-boundedness techniques and sharp L-p (L-q)-square function estimates for stochastic integrals in L-q-spaces. Under an additional invertibility assumption on A, a maximal space time L-p-regularity result is obtained as well.