# Parabolic transmission eigenvalue-free regions in the degenerate isotropic case

## TL;DR

This paper investigates the distribution of transmission eigenvalues in isotropic media with boundary-restricted refraction indices, establishing the existence of parabolic regions free of eigenvalues under certain conditions.

## Contribution

It introduces the concept of parabolic eigenvalue-free regions in the degenerate isotropic case, expanding understanding of eigenvalue distribution in this context.

## Key findings

- Existence of parabolic transmission eigenvalue-free regions.
- Conditions under which these regions occur.
- Insights into eigenvalue distribution in degenerate isotropic media.

## Abstract

We study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission eigenvalue-free regions.