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Strict 2-convexity of convex solutions to the quadratic Hessian equation
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-25 , DOI: 10.1090/proc/15454
Connor Mooney

Abstract:We prove that convex viscosity solutions to the quadratic Hessian inequality
$\displaystyle \sigma _2(D^2u) \geq 1$

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^2u) = 1$, which were proven using different methods in recent works of Guan-Qiu, McGonagle-Song-Yuan, and Shankar-Yuan.


中文翻译:

二次Hessian方程凸解的严格2-凸性。

摘要:我们证明了二次Hessian不等式的凸粘性解
$ \ displaystyle \ sigma _2(D ^ 2u)\ geq 1 $

是严格$ 2 $凸的。结果,我们获得$ C ^ 2 $了的凸性粘度解的光滑度和内在估计的简短证明,这在关秋,麦戈纳格勒·宋·袁和尚卡尔·袁的最新著作中使用了不同的方法进行了证明。 $ \ sigma _2(D ^ 2u)= 1 $
更新日期:2021-04-22
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