$C^{\infty }$ local solutions of elliptical $2-$Hessian equation in ${\mathbb{R}}^3$

Guiji Tian, Qi Wang, Chao-Jiang Xu

In this work, we study the existence of $C^{\infty }$ local solutions to $2$-Hessian equation in ${\mathbb{R}}^3$. We consider the case that the right hand side function $f$ possibl…