TY - JOUR

T1 - Polarization tensor vanishing structure of general shape

T2 - Existence for small perturbations of balls

AU - Kang, Hyeonbae

AU - Li, Xiaofei

AU - Sakaguchi, Shigeru

N1 - Funding Information:
This paper is a revised version (with the title changed) of the earlier manuscript arXiv:1911.07250. This work is supported by NRF grants No. 2017R1A4A1014735 and 2019R1A2B5B01069967, JSPS KAKENHI Grant No. 18H01126, NSF of China grant No. 11901523, and a grant from Central South University.
Publisher Copyright:
© 2021-IOS Press. All rights reserved.

PY - 2021

Y1 - 2021

N2 - The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion's existence inside a domain and used in the small volume expansion method to reconstruct small inclusions by boundary measurements. In this paper, we consider the question of the polarization tensor vanishing structure of general shape. The only known examples of the polarization tensor vanishing structure are concentric disks and balls. We prove, by the implicit function theorem on Banach spaces, that a small perturbation of a ball can be enclosed by a domain so that the resulting inclusion of the core-shell structure becomes polarization tensor vanishing. The boundary of the enclosing domain is given by a sphere perturbed by spherical harmonics of degree zero and two. This is a continuation of the earlier work (Kang, Li, Sakaguchi) for two dimensions.

AB - The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion's existence inside a domain and used in the small volume expansion method to reconstruct small inclusions by boundary measurements. In this paper, we consider the question of the polarization tensor vanishing structure of general shape. The only known examples of the polarization tensor vanishing structure are concentric disks and balls. We prove, by the implicit function theorem on Banach spaces, that a small perturbation of a ball can be enclosed by a domain so that the resulting inclusion of the core-shell structure becomes polarization tensor vanishing. The boundary of the enclosing domain is given by a sphere perturbed by spherical harmonics of degree zero and two. This is a continuation of the earlier work (Kang, Li, Sakaguchi) for two dimensions.

KW - existence

KW - implicit function theorem

KW - invisibility cloaking

KW - neutral inclusion

KW - perturbation of balls

KW - Polarization tensor

KW - polarization tensor vanishing structure

KW - weakly neutral inclusion

UR - http://www.scopus.com/inward/record.url?scp=85115874595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85115874595&partnerID=8YFLogxK

U2 - 10.3233/ASY-201651

DO - 10.3233/ASY-201651

M3 - Article

AN - SCOPUS:85115874595

VL - 125

SP - 101

EP - 132

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 1-2

ER -