紧致闭Riemann流形上带梯度项的完全非线性椭圆方程的二阶导数估计  

Second order estimates for fully nonlinear elliptic equations with gradient terms on closed Riemannian manifolds

作　　者：关波 侍述军[2] 隋哲楠 Bo Guan;Shujun Shi;Zhenan Sui

机构地区：[1]Department of Mathematics,The Ohio State University,Columbus,OH 43220,USA [2]哈尔滨师范大学数学科学学院,哈尔滨150025 [3]哈尔滨工业大学数学研究院,哈尔滨150001

出　　处：《中国科学：数学》2020年第12期1721-1732,共12页Scientia Sinica：Mathematica

基　　金：美国国家科学基金(批准号:DMS-1620086);国家自然科学基金(批准号:11971137)资助项目。

摘　　要：二阶导数先验估计是研究完全非线性椭圆方程的一个关键步骤,这是本文所关注的重点.本文考虑闭Riemann流形上一类完全非线性二阶椭圆方程,通过引入依赖解本身及其梯度的等位面的无穷远切锥,给出解的二阶导数先验估计.Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations, which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.

关 键 词：完全非线性椭圆方程 闭Riemann流形 先验估计 

分 类 号：O186.1[理学—数学]