Resonance-free Region in scattering by a strictly convex obstacle

TL;DR

This paper establishes a resonance-free region for scattering by a strictly convex obstacle with Robin boundary conditions, extending previous results known for Dirichlet and Neumann cases, and showing resonances lie below a specific cubic curve.

Contribution

It generalizes the known resonance-free regions to Robin boundary conditions, matching the cubic curve boundary previously established for Neumann conditions.

Findings

Resonances lie below a cubic curve in the complex plane.

The result extends earlier Dirichlet boundary condition findings.

It confirms the resonance-free region for Robin boundary conditions.

Abstract

We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann boundary condition. This generalizes earlier results on cubic poles free regions obtained for the Dirichlet boundary condition.