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

摘要

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. (C) 2021 Elsevier Inc. All rights reserved.