微磁学的变分原理
Variational principles of micromagnetics revisited
摘要：
我们重新审视与微磁能的最小化问题的基本变分公式，重点是杂散场对能量的贡献，这本质上是非本地的治疗。在极小化假设下，我们建立了三个不同的杂散场能量的变分原理：一个涉及磁标势的极小化极大原理和两个涉及磁矢势的极小化原理。然后，我们将我们的配方的任意形状的薄铁磁壳的降维问题。
英文摘要：
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under minimal assumptions, we establish three distinct variational principles for the stray field energy: a minimax principle involving magnetic scalar potential and two minimization principles involving magnetic vector potential. We then apply our formulations to the dimension reduction problem for thin ferromagnetic shells of arbitrary shapes.
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