Micromagnetics of thin shells

Valeriy V. Slastikov
Department of Mathematics
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract: We study a thin-shell limit of micromagnetic energy for soft small ferromagnets. The relations between thickness of the film $ t$, diameter $ l$ and magnetic exchange length $ w$ are $ t/l \rightarrow 0$ and $ tl/w^2 \lesssim 1$. We prove a $ \Gamma$-convergence of the original 3D problem to a nonlocal 2D problem.

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