The Regularity For A Class Of Monge-Ampere Equationswithsingularity

This paper is based on the research of the [1]Bernstein Theorem And Regularity For A Class of Monge-Ampere equations,our main aim is to verifythe compatibility conditions in [1] and prove the global c^? regularity of solution of a class Monge-Ampere equation with singularity near the boundary.In this paper,we study properties of the solution for the equationby using taylor expansion and inductive method.First,we rewrite the equation into the form of Euler equation the x₁-direction f₀¹=h₀???+g₀;Second,we simplify the iteration equationFinally we use technical and complicated computation to prove the Compatibility condition for the equation,and obtain the c^? global regularity of solution.