On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge–Ampère equations

AbstractIn the paper, we extend Jörgens, Calabi, and Pogorelov's theorem on entire solutions of elliptic Monge–Ampère equations to parabolic equations associated with Gauss curvature flows. Our results include Gutiérrez and Huang's previous work as a special case. Besides, we also treat the isolated singularities for parabolic Monge–Ampère equations that was firstly studied by Jörgens for elliptic case in two dimensions

Regularity of very weak solutions for elliptic equation of divergence form

AbstractIn this paper, we study the local regularity of very weak solution u∈Lloc1(Ω) of the elliptic equation Dj(aij(x)Diu)=0. Using the bootstrap argument and the difference quotient method, we obtain that if aij∈Cloc0,1(Ω), then u∈Wloc2,p(Ω) for any p<∞