Transmission eigenvalues for strictly concave domains

TL;DR

This paper proves the existence of large transmission eigenvalue-free regions in strictly concave domains and derives Weyl asymptotics with an almost optimal remainder, advancing understanding of spectral properties.

Contribution

It establishes new large eigenvalue-free regions for transmission eigenvalues in strictly concave domains and provides refined asymptotic estimates.

Findings

Existence of larger transmission eigenvalue-free regions

Weyl asymptotics with near-optimal remainder term

Enhanced spectral understanding for concave domains

Abstract

We prove that for strictly concave domains much larger transmission eigenvalue-free regions exist. As a consequence, we get Weyl asymptotics for the total counting function with an almost optimal remainder term.