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

Guiji Tian; Qi Wang; Chao-Jiang Xu

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

Analysis of PDEs 2014-06-16 v1

Authors: Guiji Tian , Qi Wang , Chao-Jiang Xu

Abstract

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 $f$ possibly vanishes, changes the sign, is positively or negatively defined. We also give the convexities of solutions which are related with the annulation or the sign of right-hand side function $f$ . The associated linearized operator are uniformly elliptic.

Keywords

2-Hessian equation elliptic equations local solutions smooth solutions linearized operator convexity sign changing

Cite

@article{arxiv.1406.3613,
  title  = {$C^\infty$ local solutions of elliptical $2-$Hessian equation in $\mathbb{R}^3$},
  author = {Guiji Tian and Qi Wang and Chao-Jiang Xu},
  journal= {arXiv preprint arXiv:1406.3613},
  year   = {2014}
}

Related papers

View all related →