Equations of Monge-Ampere type and applications

The Monge-Ampere equation is a famous fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon major breakthroughs made by the proposers in previous grant research, this project continues the investigation of fundamental problems involving Monge-Ampere type equations, such as the existence, regularity, variational and geometric properties of solutions. Further applications, in particular to affine geometry, optimal transportation and reflector design are also proposed. Expected outcomes include resolution of new problems and continuing enhancement of Australian leadership in a major area of science and technology.