The Solvability Of Dirichlet Problem For General Nonlinear Elliptic Equations

In this paper,we mainly study the Dirichlet problem of the following Hessian equa-tion with existing an admissible subsolution u (?) where ?k(?(D2u))is the k-order Elementary Symmetric Function of the eigenvalue of Hessian matrix D2u.The Dirichlet problem is one of the important boundary value problems in partial differential equations.Through the continuity method,the maximum principle and the famous Evans Krylov Theorem,we can get that the key to the existence of the solution is to give a priori estimate of the solution.