2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214065The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative space-dependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere $\mathbb S^2$. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.ProbabilityAnalysis of PDEs35Q40, 35K55, 60H15text