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Resolvent estimates for the time-harmonic Maxwell’s equations in the partially anisotropic case

Schippa, Robert

We prove resolvent estimates in $L^p$-spaces for time-harmonic Maxwell’s equations in two spatial dimensions and in three dimensions in the partially anisotropic case. In the two-dimensional case the estimates are sharp. We consider anisotropic permittivity and permeability, which are both taken to be time-independent and spatially homogeneous. For the proof we diagonalize time-harmonic Maxwell’s equations to equations involving Half-Laplacians. We apply these estimates to localize eigenvalues for perturbations by potentials and to derive a limiting absorption principle in intersections of $L^p$-spaces.

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DOI: 10.5445/IR/1000130242
Veröffentlicht am 04.03.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 03.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000130242
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 18 S.
Serie CRC 1173 Preprint ; 2021/11
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter resolvent estimates, Maxwell’s equations, limiting absorption principle
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