Neutral Inclusions, Weakly Neutral Inclusions, and an Over-determined Problem for Confocal Ellipsoids

Yong Gwan Ji, Hyeonbae Kang, Xiaofei Li, Shigeru Sakaguchi

Research output: Chapter in Book/Report/Conference proceedingChapter


An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such inclusions are of interest in relation to invisibility cloaking and effective medium theory. There have been some attempts lately to construct or to show existence of such inclusions in the form of core-shell structure or a single inclusion with the imperfect bonding parameter attached to its boundary. The purpose of this paper is to review recent progress in such attempts. We also discuss about the over-determined problem for confocal ellipsoids which is closely related with the neutral inclusion, and its equivalent formulation in terms of Newtonian potentials. The main body of this paper consists of reviews on known results, but some new results are also included.

Original languageEnglish
Title of host publicationSpringer INdAM Series
PublisherSpringer-Verlag Italia s.r.l.
Number of pages31
Publication statusPublished - 2021

Publication series

NameSpringer INdAM Series
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198


  • Confocal ellipsoids
  • Core-shell structure
  • Effective property
  • Imperfect bonding parameter
  • Invisibility cloaking
  • Neutral inclusion
  • Over-determined problem
  • Weakly neutral inclusion (=polarization tensor vanishing structure)

ASJC Scopus subject areas

  • Mathematics(all)


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