Fully nonlinear partial differential equations in optimisation and applications

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Fully nonlinear partial differential equations of Monge-Ampere type and their applications in optimal transportation have been studied intensively in the past two decades. Optimal transportation is a subject in linear optimisation. This project will develop a new theory on Monge-Ampere type equations in nonlinear optimisation, which is a much broader area with many significant applications. This project will investigate fundamental properties of solutions to this problem and explore further real-world applications. The outcomes of this project will have a substantial impact on partial differential equations and related research subjects.