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finite conductivity

European Journal of Applied Mathematics (1)

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Coated inclusions of finite conductivity neutral to multiple fields in two-dimensional conductivity or anti-plane elasticity
HYEONBAE KANG, HYUNDAE LEE
Journal:

European Journal of Applied Mathematics / Volume 25 / Issue 3 / June 2014

Published online by Cambridge University Press:

10 March 2014, pp. 329-338
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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.