Dispersive estimates for Maxwell's equations in the exterior of a sphere

verfasst von: Yan long Fang, Alden Waters
Abstract: The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the corresponding Maxwell propagator. We show that the propagator corresponding to the electric field has a global rate of decay in L¹−L^∞ operator norm in terms of time t and powers of h. In particular we show that some, but not all, polarizations of electromagnetic waves scatter at the same rate as the usual wave operator. The Dirichlet Laplacian wave operator L¹−L^∞ norm estimate should not be expected to hold in general for Maxwell's equations in the exterior of a ball because of the Helmholtz decomposition theorem.
Organisationseinheit(en): Institut für Analysis
Externe Organisation(en): University College London (UCL)
Typ: Artikel
Journal: Journal of differential equations
Band: 415
Seiten: 855-885
Anzahl der Seiten: 31
ISSN: 0022-0396
Publikationsdatum: 15.01.2025
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Analysis, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2308.00536 (Zugang: Offen)
https://doi.org/10.1016/j.jde.2024.10.024 (Zugang: Offen)