Fully nonlinear elliptic equations and applications

This proposal embodies a basic research program to study Monge-Ampere type equations and more general fully nonlinear second order elliptic partial differential equations arising in a wide range of applications in geometry, optimization, fluid mechanics, and finance. The objective is to develop new methods and techniques to study the existence, regularity, and other qualitative properties of solutions to these equations, with a view to establishing comprehensive theories. This program of research innovation will also enhance and promote the broad aims of Australian participation and leadership in key strategic areas of international science.