Nonlinear neutral inclusions: assemblages of coated ellipsoids

Abstract

The problem of determining nonlinear neutral inclusions in (electrical or thermal) conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well-known Hashin-coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids. The proposed construction is neutral for a given applied field.

Keywords

• neutral inclusions
• nonlinear dielectrics
• p-laplacian
• confocal ellipsoids