Generalised Hörmander-Rellich-Pohozhaev-Morawetz identities and their applications in spectral geometry

广义 Hörmander-Rellich-Pohozhaev-Morawetz 恒等式及其在谱几何中的应用

• 批准号: EP/W006898/1
• 负责人: Michael Levitin
• 金额: $ 6.31万
• 依托单位: University of Reading
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW006898%2F1
• 关键词: Generalised; rmander; Rellich; Pohozhaev; Morawetz

Spectral theory studies the mathematical models usually arising in wave motion, either in continuum mechanics or in quantum physics, and the abstract analogues. Most of the problems involving partial differential equations cannot be solved analytically. Spectral geometry studies the links between the underlying geometry and the spectral properties of operators, both direct and inverse.We propose to investigate some long stranding conjectures in spectral geometry, and some new problems, using the method of multipliers commonly associated with the names of Hörmander, Rellich, Pohozhaev and Morawetz. This method leads to identities which are a priori satisfied by eigenfunctions of a boundary value problem, and which can be used to extract the relevant geometric information.

谱理论研究通常在连续介质力学或量子物理学中出现的数学模型，而大多数涉及偏微分方程的抽象问题都无法通过分析来解决。算子的谱性质，包括直接的和逆的。我们建议使用通常与 Hömander 的名字相关的乘数方法来研究谱几何中的一些长链猜想以及一些新问题， Rellich、Pohozhaev 和 Morawetz。该方法导致由边值问题的本征函数先验满足的恒等式，并且可用于提取相关的几何信息。

项目成果

Two-Term Spectral Asymptotics in Linear Elasticity

• DOI: 10.1007/s12220-023-01269-y
• 发表时间: 2022-07
• 期刊: The Journal of Geometric Analysis
• 作者: Matteo Capoferri;L. Friedlander;M. Levitin;D. Vassiliev