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Entire Solutions to Generalized Parabolic k-Hessian Equations

2016
In this paper, we deal with entire solutions to the generalized parabolic k-Hessian equation of the form \(u_t = \mu (F_k(D^2 u)^{1/k})\) in \(\mathbb {R}^n \times (-\infty ,0]\). We prove that for \(1 \le k \le n\), any strictly convex-monotone solution \(u=u(x,t) \in C^{4,2}(\mathbb {R}^n \times (-\infty , 0])\) to \(u_t = \mu ( F_k(D^2 u)^{1/k ...
Saori Nakamori, Kazuhiro Takimoto
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Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations

Journal of Geometric Analysis, 2023
Dekai Zhang, Xiaohan Jia
exaly

The Convergence Analysis and Uniqueness of Blow-Up Solutions for a Dirichlet Problem of the General k-Hessian Equations

Applied Mathematics Letters, 2020
Jiafa Xu, Xinguang Zhang, Yujun Cui
exaly

Positive Radially Symmetric Entire Solutions of p-k-Hessian Equations and Systems

Mathematics, 2022
Limei Dai
exaly

On the Dirichlet Problem for General Augmented Hessian Equations

Journal of Differential Equations, 2020
Feida Jiang, Neil Trudinger
exaly

Pogorelov Type C2 Estimates for Sum Hessian Equations and a Rigidity Theorem

Journal of Functional Analysis, 2023
Changyu Ren
exaly

The Dirichlet Problem for Degenerate Hessian Equations

Communications in Partial Differential Equations, 2005
Xu-Jia Wang, Neil Trudinger
exaly