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Journal of Zhejiang University SCIENCE A

ISSN 1673-565X(Print), 1862-1775(Online), Monthly

Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions

Abstract: In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.

Key words: Landau-Lifshitz equation, Stationary condition, Hausdorff measure


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DOI:

10.1631/jzus.2007.A0949

CLC number:

O175; O48

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Received:

2006-10-07

Revision Accepted:

2007-01-17

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