A limiting absorption principle for Helmholtz systems and time-harmonic isotropic Maxwell's equations

TL;DR

This paper establishes a Limiting Absorption Principle for time-harmonic Maxwell's equations and Helmholtz systems, providing new insights into their spectral properties and resolvent behavior in L^p-L^q spaces.

Contribution

It introduces a novel L^p-L^q Limiting Absorption Principle for Maxwell operators, extending previous results to spectral parameters near the spectrum and including non-Hermitian perturbations.

Findings

Derived new L^p-L^q resolvent estimates for Maxwell operators

Extended the Limiting Absorption Principle to non-Hermitian Helmholtz systems

Improved the principle for self-adjoint Helmholtz systems

Abstract

In this work we investigate the L^p-L^q-mapping properties of the resolvent associated with the time-harmonic isotropic Maxwell operator. As spectral parameters close to the spectrum are also covered by our analysis, we obtain an L^p-L^q-type Limiting Absorption Principle for this operator. Our analysis relies on new results for Helmholtz systems with zero order non-Hermitian perturbations. Moreover, we provide an improved version of the Limiting Absorption Principle for Hermitian (self-adjoint) Helmholtz systems.