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

Zdzislaw Brzezniak, Utpal Manna

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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.
Original languageEnglish
Number of pages59
JournalCommunications in Mathematical Physics
Early online date15 Feb 2019
Publication statusE-pub ahead of print - 15 Feb 2019

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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.


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

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