流形上的k-Hessian方程的Neumann边值问题

The Neumann boundary problem for k-Hessian equations on compact manifolds

本文考虑紧致具有全脐边界的Riemann流形上k-Hessian方程的Neumann边值问题;通过对k-Hessian方程的解做零阶、一阶、二阶估计和使用连续性方法,得到流形上k-Hessian方程的Neumann边值问题的存在性结果.

In this paper,we consider the Neumann boundary problem for k-Hessian equations on compact manifolds with umbilic boundary.We establish the a priori estimates to the Neumann boundary problem for k-Hessian equations.Then by using the continuity method we arrive at an existence result for the Neumann boundary problem for k-Hessian equations.