Schiffer's Conjecture, Interior Transmission Eigenvalues and Invisibility Cloaking: Singular Problem vs. Nonsingular Problem

TL;DR

This paper explores the relationships between Schiffer's conjecture, interior transmission eigenvalues, and their implications for both singular and nonsingular acoustic invisibility cloaking problems.

Contribution

It provides new insights into the connections between mathematical conjectures and the physical problem of acoustic cloaking, highlighting differences between singular and nonsingular approaches.

Findings

Connections between Schiffer's conjecture and cloaking problems clarified.

Differences between singular and nonsingular cloaking approaches analyzed.

Potential implications for designing acoustic invisibility devices discussed.

Abstract

In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.