Some Studies Of Mean Curvature Equation And Fully Nonlinear Equation

This paper mainly contains two parts.In the first part,we will study the radial solution to k-Hessian equation with Dirichlet boundary.The uniqueness of k-Hessian equation is proved by monotone separation techniques and Pohozaev-type identity.The multiplicity of k-Hessian equation is obtained by sub-sup method and Emden-Fowler transform.In the second part,firstly,by making use of the strict convexity of domain,we construct an auxiliary function to get the uniform gradient estimate for the solution to the mean curvature flow with Neumann boundary.Introducing the additive eigenvalue problem,we study the asymptotic behavior of the mean curvature flow by maximum principle.Next,we will firstly get C1,C2 priori estimates by constructing an auxiliary function related with the boundary and then prove the existence of the solution to the real and complex lagrangian equation by the continuity method.