Essential Spectrum for Maxwell’s Equations

We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity ε , permeability μ and conductivity σ , on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely,...

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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 20; no. 5; pp. 1471 - 1499
Main Authors Alberti, Giovanni S., Brown, Malcolm, Marletta, Marco, Wood, Ian
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2019
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Domains
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Maxwell's equations
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
78A25
35P05
35Q61
35J46
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Summary:We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity ε , permeability μ and conductivity σ , on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely, the spectrum of the pencil div ( ( ω ε + i σ ) ∇ · ) , and the essential spectrum of the Maxwell pencil with constant coefficients. We expect the analysis to be of more general interest and to open avenues to investigation of other questions concerning Maxwell’s and related systems.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-019-00762-x