Singular set of viscosity solutions to Eikonal equation
报告题目(Title)：Singular set of viscosity solutions to Eikonal equation
报告人(Speaker)：李天虹 研究员（中国科学院数学与系统科学研究院)
地点(Place)：教八110
时间(Time)：2019年12月5日上午 10:30-11:30
邀请人(Inviter)：许孝精
报告摘要
The evolutionary Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian $H(P)=|P|$, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly convex Hamiltonians, therefore leading to new phenomena. In this talk, we discuss the set of singularity points of solutions in the upper half space for $C^1$ or $C^2$ initial data, with emphasis on the countability of connected components of the set. The regularity of solutions in the complement of the set of singularity points is also obtained.
