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Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise: Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise

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JournalCommunications in Mathematical Physics
DateAccepted/In press - 5 Dec 2018
DateE-pub ahead of print (current) - 15 Feb 2019
Number of pages59
Early online date15/02/19
Original languageEnglish

Abstract

In this work we study a stochastic three-dimensional Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show existence of weak martingale solutions taking values in a three-dimensional sphere $\mathbb{S}^2$ and discuss certain regularity results. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

    Research areas

  • Stochastic Landau-Lifshitz equation, weak martingale solutions, Marcus canonical form, Lévy noise

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