Singularities of solutions of Hamilton-Jacobi equations

Abstract

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.

References in corpus (6)

• Semiconcave functions in Alexandrov's geometry
• Weak KAM theorem on non compact manifolds
• Homoclinic orbits and critical points of barrier functions
• Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus
• On and beyond propagation of singularities of viscosity solutions
• Local singular characteristics on ${\mathbb{R}}^2$