Geometric variational problems and rearrangements inequalities

几何变分问题和重排不等式

• 批准号: 311685-2010
• 负责人: Burchard, Almut
• 金额: $ 1.75万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508771
• 关键词: Geometric; variational; problems; rearrangements; inequalities

Geometry is a source of both problems and insight in Analysis: Geometric flows give rise to problems in Partial Differential Equations and the Calculus of Variations; conversely, apparently purely analytic problems, such as the sharp constants in functional inequalities, can be amenable to geometric techniques such as rearrangements.

几何是分析中问题和洞察力的来源：几何流动导致偏微分方程组和变分演算中的问题；相反，表面上纯粹的分析问题，如泛函不等式中的尖锐常数，可以服从几何技术，如重排。