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.

光谱理论研究了通常在波动，连续力学或量子物理学以及抽象类似物中出现的数学模型。涉及部分微分方程的大多数问题无法分析解决。光谱几何学研究了直接和逆算子的基础几何形状与光谱特性之间的联系。我们建议研究光谱几何形状中的一些长链猜想，以及一些新问题，使用与霍尔曼德（Hörmander），雷里奇（Hörmander），雷里奇（Rellich），pohozhaev和morawetz的名称相关的乘数方法。此方法导致身份，这是边界价值问题的本征函数所满足的，并且可以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