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

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.