A Rigidity theorem for parabolic 2-Hessian equations

Yan He; Cen Pan; Ni Xiang

A Rigidity theorem for parabolic 2-Hessian equations

Analysis of PDEs 2019-06-18 v1

Authors: Yan He , Cen Pan , Ni Xiang

Abstract

In this paper, we consider the entire solutions to the parabolic $2$ -Hessian equations of the form $-u_t\sigma_2(D^2 u)=1$ in $\mathbb{R}^n\times (-\infty,0]$ . We prove some rigidity theorems for the parabolic $2$ -Hessian equations in $\mathbb{R}^n\times (-\infty,0]$ by establishing Pogorelov type estimates for $2$ -convex-monotone solutions of the parabolic $2$ -Hessian equations.

Keywords

parabolic partial differential equations parabolic equations sobolev regularity of partial differential equations

Cite

@article{arxiv.1906.06682,
  title  = {A Rigidity theorem for parabolic 2-Hessian equations},
  author = {Yan He and Cen Pan and Ni Xiang},
  journal= {arXiv preprint arXiv:1906.06682},
  year   = {2019}
}

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