A Pogorelov estimate and a Liouville type theorem to parabolic k-Hessian equations

2019/07/16 by Yan He, He, Yan, Haoyang Sheng +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1907.07006

openalex publication_date 2019/07/16 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28

Abstract

We consider Pogorelov type estimates and Liouville type theorems to parabolic k-Hessian equations of the form -u_t σ_k (D²u) =1 in ℝⁿ× (-∞, 0]. We derive that any k+1-convex-monotone solution to -u_t σ_k (D²u) =1 when u(x,0) satisfies a quadratic growth and 0

Citations

• Global C2‐Estimates for Convex Solutions of Curvature Equations

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