4 papers · 1 filter
Topology of singular set of semiconcave function via Arnaud's theorem
Tianqi Shi, Wei Cheng, Jiahui Hong
We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The pr…
Local strict singular characteristics II: existence for stationary equation on
Wei Cheng, Jiahui Hong
The notion of strict singular characteristics is important in the wellposedness issue of singular dynamics on the cut locus of the viscosity solutions. We provide an intuitive and…
Local strict singular characteristics: Cauchy problem with smooth initial data
Wei Cheng, Jiahui Hong
Main purpose of this paper is to study the local propagation of singularities of viscosity solution to contact type evolutionary Hamilton-Jacobi equation $$ D_tu(t,x)+H(t,x,D_xu(t,…
Representation formulas for contact type Hamilton-Jacobi equations
Jiahui Hong, Wei Cheng, Shengqing Hu +1
We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz' variational principle.