Coated inclusions of finite conductivity neutral to multiple fields in two dimensional conductivity or anti-plane elasticity

Abstract

We consider the problem of neutral inclusions for two-dimensional conductivity and anti-plane elasticity. The neutral inclusion, when inserted in a matrix having a uniform field, does not disturb the field outside the inclusion. The inclusion consists of a core and a shell. We show that if the inclusion is neutral to two linearly independent fields, then the core and the shell are confocal ellipses.

References in corpus (2)

• Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity Problem
• Enhancement of near-cloaking. Part II: the Helmholtz equation

Cited by in corpus (2)

• Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions
• Polarization tensor vanishing structure of general shape: Existence for small perturbations of balls