Novel Phenomena in Steklov Type Problems

Steklov 型问题中的新现象

• 批准号: EP/V051636/1
• 负责人: Jeffrey Galkowski
• 金额: $ 67.33万
• 依托单位: University College London
• 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: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV051636%2F1
• 关键词: Novel; Phenomena; Steklov; Type; Problems

The main objective of this project is to study the spectra of a large class of operators which we call Steklov Type Problems; they are also known as spectral problems for Dirichlet-to-Neumann maps. These problems have connections with electrical impedance tomography, shape analysis, and image processing as well as geometric analysis, inverse problems and fluid mechanics. These problems are also very interesting from the mathematical point of view; their systematic study has started only recently and, already, a large number of unexpected phenomena have been discovered. Our project concentrates on the further investigation and discovery of these novel phenomena.

这个项目的主要目的是研究一大类算子的谱，我们称之为Steklov型问题；它们也被称为Dirichlet-to-Neumann映射的谱问题。这些问题与电阻抗断层成像、形状分析、图像处理以及几何分析、反问题和流体力学有关。从数学的角度来看，这些问题也非常有趣；它们的系统研究最近才开始，已经发现了大量意想不到的现象。我们的项目致力于对这些新现象的进一步调查和发现。

项目成果

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies

• DOI: 10.48550/arxiv.2304.14737
• 发表时间: 2023-04
• 期刊: ArXiv
• 作者: Martin Averseng;E. Spence;J. Galkowski

Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case

经典波方法和现代规范变换：一维情况下的谱渐近

• DOI: 10.1007/s00039-023-00650-x
• 发表时间: 2023
• 期刊: Geometric and Functional Analysis
• 影响因子: 2.2
• 作者: Galkowski J

Propagation for Schrödinger operators with potentials singular along a hypersurface

沿着超曲面具有奇异势的薛定谔算子的传播

• DOI: 10.48550/arxiv.2302.08154
• 发表时间: 2023
• 作者: Galkowski J

Weyl remainders: an application of geodesic beams

韦尔余数：测地梁的应用

• DOI: 10.1007/s00222-023-01178-5
• 发表时间: 2023
• 期刊: Inventiones mathematicae
• 影响因子: 3.1
• 作者: Canzani, Yaiza;Galkowski, Jeffrey
• 通讯作者: Galkowski, Jeffrey

Geodesic Beams in Eigenfunction Analysis

特征函数分析中的测地梁

• DOI: 10.1007/978-3-031-31586-2
• 发表时间: 2023
• 作者: Canzani Y