2012
DOI: 10.1093/amrx/abs009
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Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation

Abstract: 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.

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Cited by 45 publications
(104 citation statements)
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“…The proof of this result is based the a priori estimates (4.1)-(4.10). The proof of this result is omitted since it only a relatively simple modification of the proof of a corresponding result from [9].…”
Section: Tightness Of the Laws Of Approximating Sequencementioning
confidence: 99%
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“…The proof of this result is based the a priori estimates (4.1)-(4.10). The proof of this result is omitted since it only a relatively simple modification of the proof of a corresponding result from [9].…”
Section: Tightness Of the Laws Of Approximating Sequencementioning
confidence: 99%
“…A standard procedure is to approximate the full equation by some simpler problems. In the paper [9] we used Galerkin approximation, in a series of works with Banas, Prohl and Neklyudov culminating in a monograph [7], we used the finite element approximation. Here We follow the same method as used in Brzeźniak, Goldys and Jegaraj's paper [9] but with one important addition.…”
Section: Introductionmentioning
confidence: 99%
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