关于2-Hessian方程解的全局C^2估计的一个注记

A note on global C^2 estimates of 2-Hessian equations

采用2-Hessian方程C^2估计的检验函数方法,研究了一般2-Hessian型方程σ2(λ(D2 u+B))=f(x,u,Du)的Dirichlet问题解的全局C2估计.所得结果在形式上对关于2-Hessian方程C^2估计的结果做了一般化的发展,建立了该方程解的全局C^2估计,进而得到了该方程Dirichlet问题解的存在性.

The global C^2 estimate of the solution of Dirichlet problem of the general 2-Hessian equation σ2(λ(D^2 u+B))=f(x,u,Du)is investigated by using the test function.The result of this paper is to give an extensional generalization of the form of 2-Hessian equation's C^2 estimate,establish the global C^2 estimate of the equation's solution and obtain the existence of the solution of equation's Dirichlet problem.