Stochastic and deterministic parabolic equations with bounded measurable coefficients in space and time: Well-posedness and maximal regularity

IF 2.4 2区 数学 Q1 MATHEMATICS Journal of Differential Equations Pub Date : 2024-12-02 DOI:10.1016/j.jde.2024.11.038
Pascal Auscher , Pierre Portal
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引用次数: 0

Abstract

We establish well-posedness and maximal regularity estimates for linear parabolic SPDE in divergence form involving random coefficients that are merely bounded and measurable in the time, space, and probability variables. To reach this level of generality, and avoid any of the smoothness assumptions used in the literature, we introduce a notion of pathwise weak solution and develop a new harmonic analysis toolkit. The latter includes techniques to prove the boundedness of various maximal regularity operators on relevant spaces of square functions, the parabolic tent spaces Tp. Applied to deterministic parabolic PDE in divergence form with real coefficients, our results also give the first extension of Lions maximal regularity theorem on L2(R+×Rn)=T2 to Tp, for all 1ε<p in this generality.
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
期刊最新文献
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