Regularity in time of the time-dependent Maxwell equations

Franck Assous; Patrick Ciarlet

doi:10.1016/s0764-4442(98)80158-4

Regularity in time of the time-dependent Maxwell equations

Franck Assous
, Patrick Ciarlet

Centre d'Etudes de Limeil-Valenton

Research output: Contribution to journal › Article › peer-review

Abstract

We study the regularity in time of the solution to the time-dependent Maxwell equations, in the vacuum bounded by a perfect conductor and without charges. First, we recall the results derived from the classical theory when the domain has a Lipschitz boundary. Then, when it is a polyhedron, we extend the results to both the regular and singular parts of the electromagnetic field. Last, when it is a polygon, we improve those results concerning the singular part of the field.

Translated title of the contribution	Quelques résultats sur la régularité en temps des équations de Maxwell instationnaires
Original language	English
Pages (from-to)	719-724
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	327
Issue number	8
DOIs	https://doi.org/10.1016/s0764-4442(98)80158-4
Publication status	Published - 1 Jan 1998

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AB - We study the regularity in time of the solution to the time-dependent Maxwell equations, in the vacuum bounded by a perfect conductor and without charges. First, we recall the results derived from the classical theory when the domain has a Lipschitz boundary. Then, when it is a polyhedron, we extend the results to both the regular and singular parts of the electromagnetic field. Last, when it is a polygon, we improve those results concerning the singular part of the field.

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JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

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Regularity in time of the time-dependent Maxwell equations

Abstract

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