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Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2007 Vol.8 No.6 P.949-956
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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