The Estimate Of Solution For Monge-amp(?)re Equation

A priori estimates for the solution of fully nonlinear elliptic equations is very important to study the existence and properties of solution.Since 1980s the decades in the process of Monge-Ampere equation research has experienced such a long time.In order to estimate the values of all three derivatives of the position function,L.Caffarelli.Nirenberg and J.Spruck using the Calabi method,Then,by continuity method will be consistent with the Monge-Ampere equation,det D2u = ?(x,u,D,U),x ? ?(?)Rn the existence of solutions and regularity are proved.Guan Pengfei published an important article Regularity of a class of quasilinear degenerate elliptic equations on Adv.in Math.In this article,the research has a degenerate special Monge-Ampere equation at the origin,And focus on the existence of solutions and low order regular transfer to prove the regularity of the higher.when we study the partial differential equations of fully nonlinear elliptic and parabolic,The priori estimates are very important for fully nonlinear elliptic equations,especially the C2 estimate.In this paper,we consider the convex solution of equation det D2u = f(x,Du),in Br(0)(?)R2.When the solution u is convex,the equation is elliptic.We establish the interior C2 estimate for equation det D2u = f(x,Du)with a auxiliary function in dimension n = 2.