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Time-harmonic solutions for Maxwell’s equations in anisotropic media and Bochner–Riesz estimates with negative index for non-elliptic surfaces

Mandel, Rainer; Schippa, Robert

Abstract:
We solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $L^p$ -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.

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Volltext §
DOI: 10.5445/IR/1000131189
Veröffentlicht am 06.04.2021
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: 1000131189
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 42 S.
Serie CRC 1173 Preprint ; 2021/13
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Maxwell’s equations, time-harmonic solutions, Bochner-Riesz estimates of negative index
Nachgewiesen in arXiv
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