Initial-boundary value problem for higher dimensional landau–lifshitz systems
Shijin Ding, Boling Guo · Applicable Analysis · 2004
This article is concerned with the partial regularity of the weak solutions satisfying energy inequality and monotonicity inequality to the initial-boundary value problem of Landau–Lifshitz system of ferromagnetic spin chain with Gilbert damping in higher dimensions. A generalized monotonicity inequality is derived. The singular set and its Hausdorff dimension are discussed.