Propagation of Singularities for Weak KAM Solutions and Barrier Functions
Propagation of Singularities for Weak KAM Solutions and Barrier Functions
复制标题
弱 KAM 解和势垒函数的奇点传播
DOI：
10.1007/s00220-014-2106-x
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发表时间：
2014-10-01
影响因子：
2.4
通讯作者：
Zhang, Qi
中科院分区：
文献类型：
--
作者：
Cannarsa, Piermarco;Cheng, Wei;Zhang, Qi
研究了n环面上一般力学系统Hamilton-Jacobi方程黏性解的奇异集（不可微点）的结构。首先，利用水平集方法，刻画了奇异点沿广义特征的传播。然后，我们得到了超临界情况下弱KAM解奇异性的局部传播结果。最后，我们将这一结果应用于势垒函数奇点的传播问题。
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.