TY - JOUR

T1 - An over-determined boundary value problem arising from neutrally coated inclusions in three dimensions

AU - Kang, Hyeonbae

AU - Lee, Hyundae

AU - Sakaguchi, Shigeru

N1 - Funding Information:
This work is supported by the Korean Ministry of Education, Sciences and Technology through NRF grants Nos. 2010-0017532 and 2013R1A1A1A05009699, and by Grant-in-Aid for Scientific Research (B) (# 26287020) of Japan Society for the Promotion of Science.

PY - 2016

Y1 - 2016

N2 - We consider the neutral inclusion problem in three dimensions: prove that if a coated inclusion consisting of a core and a shell is neutral to all uniform fields, then the core and the whole inclusion must be concentric balls, if the matrix is isotropic, or confocal ellipsoids if the matrix is anisotropic. We first derive an over-determined boundary value problem in the shell of the neutral inclusion, and then prove in the isotropic case that if the over-determined problem admits a solution, then the core and the whole inclusion must be concentric balls. As a consequence it is proved that the structure is neutral to all uniform fields if and only if it consists of concentric balls provided that the coefficient of the core is larger than that of the shell.

AB - We consider the neutral inclusion problem in three dimensions: prove that if a coated inclusion consisting of a core and a shell is neutral to all uniform fields, then the core and the whole inclusion must be concentric balls, if the matrix is isotropic, or confocal ellipsoids if the matrix is anisotropic. We first derive an over-determined boundary value problem in the shell of the neutral inclusion, and then prove in the isotropic case that if the over-determined problem admits a solution, then the core and the whole inclusion must be concentric balls. As a consequence it is proved that the structure is neutral to all uniform fields if and only if it consists of concentric balls provided that the coefficient of the core is larger than that of the shell.

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M3 - Article

AN - SCOPUS:85018943057

VL - 16

SP - 1193

EP - 1208

JO - Annali della Scuola normale superiore di Pisa - Classe di scienze

JF - Annali della Scuola normale superiore di Pisa - Classe di scienze

SN - 0391-173X

IS - 4

ER -