Pogorelov type $C^2$ estimates for sum Hessian equations
Analysis of PDEs
2025-04-10 v1
Abstract
In this paper, We establish Pogorelov type C2 estimates for the admissible solutions with σk(D2u) bounded from below of Sum Hessian equations. We also proved the lower bounded condition can be removed when k=n.
Cite
@article{arxiv.2504.06711,
title = {Pogorelov type $C^2$ estimates for sum Hessian equations},
author = {Pengfei Li and Changyu Ren},
journal= {arXiv preprint arXiv:2504.06711},
year = {2025}
}
Related papers
View all related →
Analysis of PDEs · Mathematics
Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem
Yue Liu, Changyu Ren
2022-04-08
Analysis of PDEs · Mathematics
Interior $C^2$ estimates for a class of sum Hessian equation
Changyu Ren, Ziyi Wang
2025-01-14
Analysis of PDEs · Mathematics
Interior Hessian estimates for sum Hessian quotient equation
Changyu Ren, Ziyi Wang
2025-10-27
Analysis of PDEs · Mathematics
Pogorelov type interior $C^2$ estimate for Hessian quotient equation and its application
Siyuan Lu, Yi-Lin Tsai
2025-05-16
Analysis of PDEs · Mathematics
Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems
Qiang Tu
2024-12-31
Analysis of PDEs · Mathematics
The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions
Weizhao Liang, Jin Yan, Hua Zhu
2025-01-14
Analysis of PDEs · Mathematics
A Pogorelov estimate and a Liouville type theorem to parabolic $k$-Hessian equations
Yan He, Haoyang Sheng, Ni Xiang
2019-07-17
Analysis of PDEs · Mathematics
Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$
Chenyang Liu, Jing Mao, Yating Zhao
2022-02-01
Analysis of PDEs · Mathematics
Pogorelov interior estimates for general sum-type Hessian equations
Weisong Dong, Sirui Xu, Ruijia Zhang
2026-03-17
Analysis of PDEs · Mathematics
Interior estimates of derivatives and a Liouville type theorem for Parabolic $k$-Hessian equations
Jiguang Bao, Jiechen Qiang, Zhongwei Tang, Cong Wang
2023-01-16
Analysis of PDEs · Mathematics
The Pogorelov estimates for degenerate curvature equations
Heming Jiao, Yang Jiao
2024-04-12
Analysis of PDEs · Mathematics
Remarks on the Pogorelov type estimate for the degenerate $k$-Hessian equation
Yasheng Lyu
2026-02-27
Analysis of PDEs · Mathematics
The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds
Xiaojuan Chen, Juhua Shi, Xiaocui Wu, Kang Xiao
2022-10-26
Analysis of PDEs · Mathematics
Admissible solutions to augmented nonsymmetric $k$-Hessian type equations II. A priori estimates and the Dirichlet problem
Bang Tran Van, Ngoan Ha Tien, Tho Nguyen Huu, Tien Phan Trong
2022-04-06
Analysis of PDEs · Mathematics
A Rigidity theorem for parabolic 2-Hessian equations
Yan He, Cen Pan, Ni Xiang
2019-06-18
Analysis of PDEs · Mathematics
Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions
Xinqun Mei, Jin Yan
2026-04-28
Analysis of PDEs · Mathematics
$\mathrm{C}^2$ estimates for general $p$-Hessian equations on closed Riemannian manifolds
Yuxiang Qiao
2025-09-11
Analysis of PDEs · Mathematics
The Dirichlet problem for a class of Hessian type equations
Heming Jiao, Tingting Wang
2016-05-06
Analysis of PDEs · Mathematics
The Neumann problem for a class of degenerate Hessian quotient type equations
Jiabao Gong, Qiang Tu
2026-04-13
Analysis of PDEs · Mathematics
Serrin-type Overdetermined problems in $\mathbb H^n$
Zhenghuan Gao, Xiaohan Jia, Jin Yan
2022-01-13
Analysis of PDEs · Mathematics
Second order estimates for equations with sums of Hessian operators on Hermitian manifolds
Weisong Dong, Ruijia Zhang
2026-03-20
Analysis of PDEs · Mathematics
Non-polynomial entire solutions to $\sigma_{k}$ equations
Micah Warren
2015-04-20
Analysis of PDEs · Mathematics
$C^2$ estimates for $k$-Hessian equations and a rigidity theorem
Ruijia Zhang
2025-02-18
Analysis of PDEs · Mathematics
On Counterexamples to Interior $C^2$ Estimates for Monge-Amp\`ere Type Equations
Cheuk Yan Fung
2026-02-23
Analysis of PDEs · Mathematics
Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients
Francesca Anceschi, Sergio Polidoro, Maria Alessandra Ragusa
2019-07-31