Regularity of weak solutions to the Landau-Lifshitz system in bounded regular domains

Abstract

In this paper, we study the regularity, on the boundary, of weak solutions to the Landau-Lifshitz system in the framework of the micromagnetic model in the quasi-static approximation. We establish the existence of global weak solutions to the Landau-Lifshitz system whose tangential space gradient on the boundary is square integrable.