Pogorelov type estimates for (n-1)-Hessian equations and related rigidity theorems

2024/05/05 by Tu, Qiang
#35B45 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.02939

Abstract

In this paper, we establish Pogorelov type C² estimates for admissible solutions to the Dirichlet problem of (n-1)-Hessian equation based on a concavity inequality, which is inspired by the Lu-Tsai's work on the global curvature estimates for the n-1 curvature equation. As an application, we apply such estimates to obtain a rigidity theorems for admissible solutions of (n-1)-Hessian equation only under quadratic growth conditions. This result gives a positive answer to a open problem for k-Hessian equation, which is proposed by Chang-Yuan, in case k=n-1.

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