FRG Collaborative Proposal: Eigenfunctions of the Laplacian

FRG 合作提案：拉普拉斯算子的本征函数

• 批准号: 0354386
• 负责人: Christopher Sogge
• 金额: $ 40.7万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354386&HistoricalAwards=false
• 关键词: FRG; Collaborative; Proposal; Eigenfunctions; Laplacian

Collaborative proposal DMS 0354386/0354539/0354668PIs: C.Sogge, S.Zelditch (Johns Hopkins)/D.Tataru, M.Zworski(U California, Berkeley)/H.Smith (U Washington)Title: Eigenfunctions of the LaplacianABSTRACTThis proposal is concerned with estimates of solutions of waveequations on (both compact and non-compact) Riemannian manifolds, possibly with boundary. We are interested in how thegeometry, the boundary and the regularity of the metric influencecertain basic estimates. Problems of this kind arise both in thestudy of local and global existence of solutions of nonlinear waveequations and in the study of eigenfunctions of Laplacians inquantum chaos. Although these topics are widely separated in theirphysical origins, the relevant mathematics is closely related andthe techniques and insights in the two areas cross fertilize ina fruitful way. Each of the PIs is an expert one of these areas.By pooling our knowledge through a FRG grant we shall be able to make significant progress in these fields as wellas possibly in related ones such as general relativity theory.Eigenfunctions are the building blocks of functions. Understandingtheir basic size and concentration properties helps us solve new differential equations. In the other direction, techniques fromthe study of nonlinear wave equations have recently been usedto prove new results about eigenfunctions. This proposal isabout continuing this cross-fertilization of related fields.

Collaborative proposal DMS 0354386/0354539/0354668PIs: C.Sogge, S.Zelditch (Johns Hopkins)/D.Tataru, M.Zworski(U California, Berkeley)/H.Smith (U Washington)Title: Eigenfunctions of the LaplacianABSTRACTThis proposal is concerned with estimates of solutions of waveequations在（紧凑型和非压缩）Riemannian歧管上，可能具有边界。 我们对计量影响的基本估计值的几何，边界和规则性感兴趣。这种问题既是在局部和全球存在的非线性波动式解决方案以及在laplacians征询征征的本征征的研究中出现的。尽管这些主题在其物理起源中被广泛分开，但相关的数学密切相关，并且在这两个领域的技术和见解交叉施肥。 每个PI都是这些领域的专家。通过通过FRG赠款汇总我们的知识，我们将能够在这些领域中取得重大进展，以及可能在相关的领域（例如一般相对论理论）。eigenfunctions是功能的基础。 了解您的基本规模和集中属性有助于我们解决新的微分方程。 在另一个方向上，最近已使用了非线性波方程研究的技术来证明有关本征函数的新结果。 该提案iSabout继续对相关字段的交叉施加。