Singularity and regularity for Monge-Ampere type equations

The Monge-Ampere equation, as a premier nonlinear partial differential equation, arises in several areas includinggeometry, physics, and optimal transportation. Many important problems and applications are related to theregularity of solutions, which are obstructed by singularities. This project aims to classify the geometry of thesingular sets, and to establish a comprehensive regularity theory for general Monge-Ampere type equations byusing innovative approaches and developing cutting-edge technologies in partial differential equations. Expectedoutcomes include the resolution of outstanding open problems. This project will significantly enhance Australiasleadership and expertise in a major area of mathematics and applications.