Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains.

Andrea Bonito (1) , Jean-Luc Guermond (1) , Francky Luddens (2)

1 TAMU - Department of Mathematics [Texas]
2 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coe cients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coe cients.

Keywords: Maxwell equations; elliptic regularity; discontinuous coe cients; Lip- schitz domains

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Andrea Bonito, Jean-Luc Guermond, Francky Luddens. Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains.. Journal of Mathematical Analysis and Applications, 2013, 408 (2), pp.498-512. ⟨hal-01024489⟩