The Oblique Boundary Value Problem For Special Lagrangian Equations

Elliptic partial differential equation is a class of important partial differential equation,the boundary value problem is also a classical subject in the research of modern partial differential equation.The boundary conditions in the boundary value problem have Dirichlet conditions,Neumann conditions,oblique derivative conditions and so on.There are several methods to study the boundary prob-lem of elliptic partial differential equations,such as maximum principle,continuity method,a priori estimate.In this paper,we mainly study the oblique boundary val-ue problem of Special Lagrangian equation.By selecting the appropriate auxiliary function,we give tht C0,C1,C2 estiuates of the solution respectively.According to the concavity of the operator,we obtain the estimate of C2,a.Finally,we obtain the existence of the solution by the standard continuity method.