Estimation Of Solutions Of Two-dimensional M-A Equation

Monge-Ampere equation(abbreviated as M-A)is a class of Nonlinear Elliptic Equa-tions in geometry,it is the basic form for det D2u = f(x,u,Du).The priori estimation of fully nonlinear elliptic equation is very important,especially the C2 estimation.In this article,the convex solutions of M-A equation det D2u = f(x,u),BR(O)(?)R2 is considered in the dimension n = 2.When the solution u is convex,the M-A equation is elliptic.Here by an auxiliary function ? respectively to the solution of internal C2 estimation are discussed.When f(x)= 1,the convex solution u of det D2u = 1 on the boundary is zero(often referred to as the Dirichlet problem).The full text is divided into three chapters,as follows:In the first chapter,we briefly introduce the research background and progress of M-A equation,and some notations and definitions used in this article.In the second chapter,we introduce the propositions and related basic knowledge.In the third chapter,we give the theorems and conclusions related to M-A equation det D2u = f(x,u),as well as the detailed proof process.