Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator

The motivation for the work done in this thesis is the resolution of an eigenvalue problem for the 2-Hessian operator. In order to be in a position to address this problem, several subproblems have to be examined. We discuss the Dirichlet problem for the two dimensional Monge-Ampere equation and the eigenvalue problem for the Monge-Ampere operator. Several strategies for the resolution of the problem are explored.