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The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent 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 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.

We study transition semigroups and Kolmogorov equations corresponding to stochastic semilinear equations on a Hilbert space H. It is shown that the transition semigroup is strongly continuous and locally equicontinuous in the space of polynomially increasing continuous functions on H when endowed with the so-called mixed topology. As a result we characterize cores of certain second order differential operators in such spaces and show that they have unique extensions to generators of strongly continuous semigroups. Academic Press

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