基于最优运输的度量空间ABP估计

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-09-08 DOI:10.1016/j.jde.2025.113757

Bang-Xian Han

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引用次数: 0

摘要

利用最优传输理论，在具有合成黎曼里奇曲率下界的度量测度空间上建立了一个尖锐的ABP型估计，并证明了一些包含泛函ABP估计的几何不等式和泛函不等式。我们的结果不仅扩展了ABP估计的边界，而且为非光滑框架下的Jacobi场计算提供了一种有效的替代方法，对非光滑几何分析中的许多问题具有潜在的应用价值。

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ABP estimate on metric measure spaces via optimal transport

By using optimal transport theory, we establish a sharp Alexandroff–Bakelman–Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities including a functional ABP estimate. Our result not only extends the border of ABP estimate, but also provides an effective substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis.

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来源期刊

Journal of Differential Equations 数学-数学

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