Spectral properties of the Neumann-Poincar\'e operator and cloaking by anomalous localized resonance for the elasto-static system

Autor:	Ando, Kazunori, Ji, Yong-Gwan, Kang, Hyeonbae, Kim, Kyoungsun, Yu, Sanghyeon
Rok vydání:	2015
Předmět:	Mathematics - Analysis of PDEs 35J47 (primary) 35P05 (secondary)
Druh dokumentu:	Working Paper
Popis:	We first investigate spectral properties of the Neumann-Poincar\'e (NP) operator for the Lam\'e system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for Laplace operator. We then show that even if elasto-static NP operator is not compact even on smooth domains, its spectrum consists of eigenvalues which accumulates to two numbers determined by Lam\'e constants. We then derive explicitly eigenvalues and eigenfunctions on disks and ellipses. We then investigate resonance occurring at eigenvalues and anomalous localized resonance at accumulation points of eigenvalues. We show on ellipses that cloaking by anomalous localized resonance takes place at accumulation points of eigenvalues. Comment: 33 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1510.00989 Zobrazit plný text záznamu View this record from Arxiv