STRICT 2-CONVEXITY OF CONVEX SOLUTIONS TO THE QUADRATIC HESSIAN EQUATION

被引：2

作者：

Mooney, Connor ^{[1
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 06期

关键词：

Sigma-2; equation; regularity;

D O I：

10.1090/proc/15454

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that convex viscosity solutions to the quadratic Hessian inequality sigma(2 )(D(2)u) >= 1 are strictly 2-convex. As a consequence we obtain short proofs of smoothness and interior C-2 estimates for convex viscosity solutions to sigma(2)(D(2)u) = 1, which were proven using different methods in recent works of Guan-Qiu, McGonagle-Song-Yuan, and Shankar-Yuan.

引用

页码：2473 / 2477

页数：5

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