A Lagrangian Approach to Weakly Coupled Hamilton-Jacobi Systems

A Lagrangian Approach to Weakly Coupled Hamilton-Jacobi Systems
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DOI：
10.1137/15m1010841
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发表时间：
2015-03
期刊：
SIAM J. Math. Anal.
影响因子：
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通讯作者：
Hiroyoshi Mitake;A. Siconolfi;H. Tran;N. Yamada
Hiroyoshi Mitake;A. Siconolfi;H. Tran;N. Yamada
中科院分区：
其他
文献类型：
--
作者：
Hiroyoshi Mitake;A. Siconolfi;H. Tran;N. Yamada

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我们研究了一类弱耦合Hamilton-Jacobi系统，具体目的是在弱KAM理论的精神下进行定性分析。我们的主要成就是定义了一个家庭的相关行动泛函包含拉格朗日从系统的哈密顿对偶。我们用它们来表征，通过适当的估计，系统的所有子解，并明确表示一些子解享受额外的极大值属性。我们分析的一个关键步骤是把问题放在一个合适的随机框架中。只需要一些基本的测量理论的知识，并介绍是无概率背景的读者访问。
We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing the Lagrangians obtained by duality from the Hamiltonians of the system. We use them to characterize, by means of a suitable estimate, all the subsolutions of the system, and to explicitly represent some subsolutions enjoying an additional maximality property. A crucial step for our analysis is to put the problem in a suitable random frame. Only some basic knowledge of measure theory is required, and the presentation is accessible to readers without background in probability.