# Cloaking for a quasi-linear elliptic partial differential equation

## TL;DR

This paper explores cloaking techniques for quasi-linear elliptic PDEs, demonstrating perfect, approximate, and isotropic cloaks through various mathematical schemes, extending prior linear PDE cloaking research.

## Contribution

It introduces new cloaking methods for quasi-linear PDEs, including regular and homogenized isotropic cloaks, expanding cloaking theory beyond linear models.

## Key findings

- Perfect cloaks via singular transformations
- Approximate cloaks using regular transformations
- Isotropic cloaks through homogenization

## 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.