A rigidity theorem for parabolic 2-Hessian equations. (English) Zbl 1504.35169
Summary: In this paper, we consider the entire solution to the parabolic \(2\)-Hessian equation \(-u_t\sigma_2(D^2 u)=1\) in \(\mathbb{R}^n\times (-\infty,0]\). We prove a rigidity theorem for the parabolic \(2\)-Hessian equation in \(\mathbb{R}^n\times (-\infty,0]\) by establishing Pogorelov type estimates for \(2\)-convex-monotone solutions.
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B08 | Entire solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35K96 | Parabolic Monge-Ampère equations |
Keywords:
rigidity theorem; parabolic 2-Hessian equation; 2-convex-monotone solution; Pogorelov-type estimatesReferences:
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