Cloaking for a quasi-linear elliptic partial differential equation

Abstract

In this article we consider cloaking for a quasi-linear elliptic partial differential equation of divergence type defined on a bounded domain in ${\mathbb{R}}^N$ for $N=2,3$. We show that a perfect cloak can be obtained via a singular change of variables scheme and an approximate cloak can be achieved via a regular change of variables scheme. These approximate cloaks though non-degenerate are anisotropic. We also show, within the framework of homogenization, that it is possible to get isotropic regular approximate cloaks. This work generalizes to quasi-linear settings previous work on cloaking in the context of Electrical Impedance Tomography for the conductivity equation.