Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem
Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem
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Pogorelov 类型 $C^2$ 估计 Sum Hessian 方程和刚性定理
DOI：
10.1016/j.jfa.2022.109726
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发表时间：
2023
影响因子：
1.7
通讯作者：
Changyu Ren
中科院分区：
文献类型：
--
作者：
Yue Liu;Changyu Ren
本文主要研究和Hessian方程Dirichlet问题解的Pogorelov型C^2 $估计。在一定条件下，分别建立了k-凸解和容许解的Pogorelov型C^2估计.进一步，我们应用这样的估计得到了欧氏空间中Sum Hessian方程的k-凸解的刚性定理。
We mainly study Pogorelov type $C^2$ estimates for solutions to the Dirichlet problem of Sum Hessian equations. We establish respectively Pogorelov type $C^2$ estimates for $k$-convex solutions and admissible solutions under some conditions. Furthermore, we apply such estimates to obtain a rigidity theorem for $k$-convex solutions of Sum Hessian equations in Euclidean space.