Stochastic maximal L^p(L^q)-regularity for second order systems with periodic boundary conditions

2021/06/02 by Agresti, Antonio, Veraar, Mark · 2 citations
#42B37 #46F10 #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 60H15 #Probability (math.PR) #Secondary: 35B65

paper · doi:10.48550/arxiv.2106.01274

Abstract

In this paper we consider an SPDE where the leading term is a second order operator with periodic boundary conditions, coefficients which are measurable in (t,ω), and Hölder continuous in space. Assuming stochastic parabolicity conditions, we prove L^p((0,T)× Ω, t^κ d t;H^σ,q(\mathbbT^d))-estimates. The main novelty is that we do not require p=q. Moreover, we allow arbitrary σ∈ ℝ and weights in time. Such mixed regularity estimates play a crucial role in applications to nonlinear SPDEs which is clear from our previous work. To prove our main results we develop a general perturbation theory for SPDEs. Moreover, we prove a new result on pointwise multiplication in spaces with fractional smoothness.

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• A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise
• The stochastic Keller--Segel system in critical spaces

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