| Computational Mathematics |
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| Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions |
| FANG Dao-yuan, LI Tai-long, XUE Ru-ying |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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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.
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Received: 07 October 2006
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