Sharp Upper Bounds for a Singular Perturbation Problem Related to Micromagnetics
نویسنده
چکیده
We construct an upper bound for the following family of functionals {Eε}ε>0, which arises in the study of micromagnetics: Eε(u) = ∫ ε|∇u|2 + 1 ε ∫ R2 |Hu |2. Here is a bounded domain in R2, u ∈ H1( , S1) (corresponding to the magnetization) and Hu , the demagnetizing field created by u, is given by { div (ũ + Hu) = 0 in R2 , curl Hu = 0 in R2 , where ũ is the extension of u by 0 in R2 \ . Our upper bound coincides with the lower bound obtained by Rivière and Serfaty. Mathematics Subject Classification (2000): 49J45 (primary); 35B25, 35J20 (secondary).
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تاریخ انتشار 2007