The Supreme Challenges of Supremal Functionals

至高泛函的最高挑战

• 批准号: EP/X017206/1
• 负责人: Roger Moser
• 金额: $ 30.93万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX017206%2F1
• 关键词: Supreme; Challenges; Supremal; Functionals

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.

变化的计算是如何最大程度地减少或最大化某些数量的理论。大多数现有理论都涉及某些值的平均值（或积分）（进而取决于功能及其衍生物）的数量。关于如何最大程度地减少最大值的问题的理论较小，但目前仅涵盖特定情况。该项目旨在从可以为数值实现设计的分析角度来开发具有更大范围的新方法。