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

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.