C^(2)estimates for a class of degenerate k-Hessian equations with gradient terms on closed Hermitian manifolds  

封闭Hermitian流形中一类带梯度项的退化k-Hessian方程的C^(2)估计

作　　者：WU Hanqing XU Lu 吴瀚清;徐露(湖南大学数学学院,湖南长沙410082)

机构地区：[1]School of Mathematics,Hunan University,Changsha 410082,China

出　　处：《纯粹数学与应用数学》2025年第1期25-45,共21页Pure and Applied Mathematics

基　　金：国家自然科学基金(12171143).

摘　　要：In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.本文中将解决在封闭的Hermitian流形上的一类退化k-Hessian方程的k-convex解的C^(2)估计.这类方程的右端函数与方程未知函数以及它的梯度有关.本文将推广前人的结果以得到该方程的C^(0)估计,而后得到该方程的“HMW估计”,使得方程满足使用爆破分析的条件,以此得到方程的梯度估计和二阶估计.该估计将对研究该方程的解的存在性产生极大的帮助.

关 键 词：C^(2)estimates degenerate k-Hessian equation closed Hermitian manifold 

分 类 号：O175.2[理学—数学]