Games associated with products of eigenvalues of the Hessian

Abstract

We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length goes to zero, the value functions of the games converge uniformly to a viscosity solution of the partial differential equation. The classical Monge-Ampère equation is an important example under consideration.

Keywords

• eigenvalues of the hessian
• games
• monge-ampère equations