Convexity Estimates For The Solutions Of A Class Of Elliptic Hessian Equations

Geometric properties of solution is a pure problem in the theory of partial differential equations,and convexity as important geometric properties has been im-portant hot topic in the field of elliptic partial differential equation.Monge-Ampere equation det(D2u)= f(u)is the important fully nonlinear partial differential equa-tion.In this paper,for the strictly convex solutions of the Monge-Ampere equation with homogeneous Dirichlet boundary value condition,we find an auxiliary func-tion which is related with curvature of the level sets of u and satisfies a differential inequality.By the maximum principle,we can prove the fact that the function at-tains its maximum on the boundary.And under certain conditions,some geometric characterizations of domain ? are performed.