This is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton–Jacobi equations in the past decades. We also review further applications of the theory to various fields such as Riemannian geometry, Hamiltonian dynamical systems and partial differential equations.

中文翻译：

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Hamilton–Jacobi方程解的奇异性

这是一份关于过去几十年来对Hamilton-Jacobi方程的粘度解的奇异性传播进行定量分析的调查论文。我们还将回顾该理论在诸如黎曼几何，哈密顿动力学系统和偏微分方程等各个领域的进一步应用。