一类拟线性退化椭圆方程Dirichlet问题粘性解的C^α正则性

The Cα-Regularity of Viscosity Solutions of Dirichlet Problems for Quasi-Linear Degenerate Elliptic Equations

讨论了一类拟线性退化椭圆方程 Dirichlet问题 - Tr[a(x) D2 u]+ H (x,u,Du) =0 ,x∈Ω u =ψ,x∈ Ω粘性解的 Cα 正则性 ,证明了当方程及边界满足一定条件时 ,若边值ψ(x)∈ Cα( Ω ) ,则粘性解 u(x)∈ Cα(Ω ) .

The C α regularity of viscosity solutions of Dirichl et problems for quasi linear degenerate elliptic equations -Tr+H(x,u,Du)=0, x∈Ω u=ψ, x ∈Ω is discussed. It was proved that, if the boundary value φ(x)∈C α(Ω), the viscosity solutions u(x)∈C α(Ω).