In this paper we prove local existence and uniqueness of regular solutions for a quasistatic model arising in micromagnetism theory. Moreover we show global existence of regular solutions for small data in the 2D case for the Landau-Lifschitz equation. These results extend those already obtained by the authors in the whole space.
"Regular solutions for Landau-Lifschitz equation in a bounded domain." Differential Integral Equations 14 (2) 213 - 229, 2001. https://doi.org/10.57262/die/1356123353