4 papers
Error estimates for numerical approximations of a nonlinear gradient flow model
Jerome Droniou, Kim-Ngan Le, Huateng Zhu
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient d…
Classification of positive solutions to a class of Laplace equations with a gradient term
Jingbo Dou, Benfeng Shi, Tian Wu +1
In this paper, we investigate positive solutions to a class of Laplace equations with a gradient term on a complete, connected, and noncompact Riemannian manifold \((M^n,g)\) with…
Neumann Problems for Elliptic and Parabolic Sum Hessian Equations
Weizhao Liang, Jin Yan, Hua Zhu
This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori estimates for -admissible solutions in almost convex and unif…
The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions
Weizhao Liang, Jin Yan, Hua Zhu
In this paper, we primarily study the Pogorelov-type estimates for -convex solutions of the sum Hessian equation under the assumption of semi-convexity, and apply thes…