一类隐式偏微分方程的Dirichlet问题

The Dirichlet problem of implicit partial differential equations

给出了一类隐式偏微分方程的Dirichlet问题:g(x,Du(x))=0,a.e.x∈Ω,u(x)=φ(x),x∈ Ω,的弱解的存在性的充分条件.

In this article,it is given that sufficient conditions for the existence of weak solutions to the vectorial Hamilton-Jacobi equations with Dirichlet boundary condition:g(x,Du(x))=0,a.e.x∈Ω, u(x)=φ(x),x∈Ω.