论文标题
严格的$ 2 $ - 凸面解决方案的概述到二次Hessian方程
Strict $2$-convexity of convex solutions to the quadratic Hessian equation
论文作者
论文摘要
我们证明，对二次Hessian不平等的凸粘度解决方案$σ_2（d^2u）\ geq 1 $严格$ 2 $ -CONVEX。结果，我们获得了简短的光滑度和内部$ c^2 $估算的估计值，用于$σ_2（d^2u）= 1 $，在Guan-qiu \ cite {gq}的最新方法中证明了这些方法，这些方法已证明了这些方法{gq}，McGonagle-Song-song-song-yuan \ cite {msy} syan and shankArn-shankArn-shankArn-cite} and shankArn-cite。
We prove that convex viscosity solutions to the quadratic Hessian inequality $σ_2(D^2u) \geq 1$ are strictly $2$-convex. As a consequence we obtain short proofs of smoothness and interior $C^2$ estimates for convex viscosity solutions to $σ_2(D^2u) = 1$, which were proven using different methods in recent works of Guan-Qiu \cite{GQ}, McGonagle-Song-Yuan \cite{MSY} and Shankar-Yuan \cite{SY2}.
