Regularity properties of the solutions to the 3D Maxwell–Landau–Lifshitz system in weighted Sobolev spaces

Abstract

This paper is concerned with special regularity properties of the solutions to the Maxwell–Landau–Lifshitz (MLL) system describing ferromagnetic medium. Besides the classical results on the boundedness of ∂ t m , ∂ t E and ∂ t H in the spaces L ∞ ( I , L 2 ( Ω ) ) and L 2 ( I , W 1 , 2 ( Ω ) ) we derive also estimates in weighted Sobolev spaces. This kind of estimates can be used to control the Taylor remainder when estimating the error of a numerical scheme.