Propagation of Singularities for Weak KAM Solutions and Barrier Functions

被引：10

作者：

Cannarsa, Piermarco ^{[1
]}

Cheng, Wei ^{[2
]}

Zhang, Qi ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[3] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2014年 / 331卷 / 01期

关键词：

Viscosity Solution; Homoclinic Orbit; Jacobi Equation; Viscosity Subsolution; Local Maximum Point;

D O I：

10.1007/s00220-014-2106-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper studies the structure of the singular set (points of nondifferentiability) of viscosity solutions to Hamilton-Jacobi equations associated with general mechanical systems on the n-torus. First, using the level set method, we characterize the propagation of singularities along generalized characteristics. Then, we obtain a local propagation result for singularities of weak KAM solutions in the supercritical case. Finally, we apply such a result to study the propagation of singularities for barrier functions.

引用

页码：1 / 20

页数：20

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