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

Hyeonbae Kang, Hyundae Lee, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1193-1208
Number of pages16
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume16
Issue number4
Publication statusPublished - 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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