Singular domain deformation and analysis on elliptic operators in elasticity and electromagnetism

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400153
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Hokkaido University
• Principal Investigator: Jimbo Shuichi 北海道大学, 理学(系)研究科(研究院), 教授 (80201565)
• Co-Investigator(Kenkyū-buntansha): HONDA NAOFUMI 北海道大学, 大学院理学研究院, 教授 (00238817) ; TONEGAWA YOSHIHIRO 東京工業大学, 理工学研究科, 教授 (80296748)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 特異的領域変形 / 楕円型作用素 / 固有値問題

Outline of Final Research Achievements

I studied spectra of elliptic operators for regularly or singularly deformed domain (Lame operator, Stokes operator, Maxwell operator). (i) I studied polynomial solutions, rational type solutions with their structures of homogeneous Stokes and Elastic equations (with H.Ito, N.Honda), (ii) I obtained spectral Hadamard variational formula of Stokes operator, Maxwell operator for regularly perturbed domain for Dirichlet and Slip type boundary condition (with E. Ushikoshi). I obtained an elaborate behaviors of eigenvalues for Maxwell operator, (iii) I studied elaborate behaviors of eigenvalues of Lame or Maxwell operators in a domain with small hole, (iv) I obtained elaborate behaviors of eigenfrequencies of elastic body composed of several thin rod.

Free Research Field

応用解析学, 偏微分方程式