Local minimizers in micromagnetics and related problems

John M. Ball, Ali Taheri, and M. Winter

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Submission date: 08. Jan. 2001
Pages: 28
published in: Calculus of variations and partial differential equations, 14 (2002) 1, p. 1-27 
DOI number (of the published article): 10.1007/s005260100085
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Abstract:
Let be a smooth bounded domain and consider the energy functional

Here is a small parameter and the admissible function m lies in the Sobolev space of vector-valued functions and satisfies the pointwise constraint |m(x)|=1 for a.e. . The induced magnetic field is related to m via Maxwell's equations and the function is assumed to be a sufficiently smooth, non-negative energy density with a multi-well structure. Finally is a constant vector. The energy functional arises from the continuum model for ferromagnetic materials known as micromagnetics developed by W.F. Brown.