Several Problems In Nonlinear Partial Differential Equations

Like many models for geometry and physics problems,the existence and the unique-ness of a solution are the most important research topics in nonlinear partial differential equations.In this paper,we study the properties of solutions to the second order fully nonlinear elliptic partial differential equations,using the special Lagrangian equations as an example.Specifically,we study the Neumann boundary problems for special La-grangian equations with critical phases in the real bounded convex domain and in the complex bounded strictly pseudoconvex domain,respectively.We first obtain the apri-ori estimates using the maximum principle,then prove the existence theorem using the method of continuity.