Monge-Ampere equations and applications

蒙日-安培方程是一个重要的全非线性偏微分方程，在几何、物理和应用科学中有着重要的应用。本项目旨在解决涉及蒙日-安培型方程及其应用的具有挑战性的问题。项目目标是通过引入新思想和发展创新的前沿技术，为应用科学中出现的蒙日-安培型方程解建立新的正则性理论和奇点剖面分类。预期的结果包括解决悬而未决的问题，并继续提高澳大利亚在主要数学领域的领导地位和专业知识。

The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere type equation arising in applied sciences, by introducing new ideas and developing innovative cutting-edge techniques. Expected outcomes include resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.