瓦瑟斯坦空间上的艾克纳方程粘度解

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-05-27 DOI:10.1007/s00245-024-10145-2

H. Mete Soner, Qinxin Yan

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引用次数: 0

摘要

具有可分离结构的均值场控制问题的动态程序方程是瓦瑟斯坦空间上的 Eikonal 型方程。使用线性导数进行标准微分可直接扩展经典粘度理论。我们利用量纲空间上索博列夫规范的傅立叶表示法，结合有限维理论的标准技术，证明了半连续子解和超解之间的比较结果，从而获得了值函数的独特特征。

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Viscosity Solutions of the Eikonal Equation on the Wasserstein Space

Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity theory. We use Fourier representation of the Sobolev norms on the space of measures, together with the standard techniques from the finite dimensional theory to prove a comparison result among semi-continuous sub and super solutions, obtaining a unique characterization of the value function.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.