On the structure of the geometric tangent cone to the Wasserstein space

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-06-10 DOI:10.1016/j.jde.2025.113520

Averil Aussedat

引用次数: 0

Abstract

This article focuses on the metric orthogonal of the geometric tangent cone to the Wasserstein space. Some algebraic and topological properties are given, as well as a complete characterization and weak closedness property in dimension 1. It is shown that in general, the directional derivative of the Wasserstein distance is not sufficient to differentiate between the tangent cone and its orthogonal. To conclude, a general Helmholtz-Hodge decomposition is proved for measure fields.

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论Wasserstein空间的几何切锥结构

本文主要研究几何切锥与Wasserstein空间的度量正交。给出了它的一些代数和拓扑性质，以及它在1维上的完全刻画和弱闭性。一般情况下，Wasserstein距离的方向导数不足以区分切锥与其正交锥。最后，证明了测度域的一般Helmholtz-Hodge分解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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