The Supreme Challenges of Supremal Functionals

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The calculus of variations is the theory of how to minimise or maximise certain quantities. Most of the existing theory deals with quantities given in terms of the average (or integral) of certain values (which in turn depend on a function and its derivatives). There is a smaller body of theory on the question of how to minimise the maximum instead, but it currently covers only specific cases. This project aims to develop new methods with a greater scope, from an analytic point of view that can inform the design of numerical realisations.