Sharp upper bounds for a singular perturbation problem related to micromagnetics

Arkady Poliakovsky

Sharp upper bounds for a singular perturbation problem related to micromagnetics

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4 Scopus citations

Abstract

We construct an upper bound for the following family of functionals {E_ε}_ε>0, which arises in the study of micromagnetics: E_ε(u)=∫Ωε ∇u ² + 1/ε ∫ℝ² H_u ². Here Ω is a bounded domain in ℝ², u ∈ H¹(Ω, S¹) (corresponding to the magnetization) and H_u, the demagnetizing field created by u, is given by Formula is presented, where ũ is the extension of u by 0 in ℝ²\Ω. Our upper bound coincides with the lower bound obtained by Rivière and Serfaty.

Original language	English
Pages (from-to)	673-701
Number of pages	29
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	6
Issue number	4
State	Published - 1 Dec 2007
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

Cite this

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abstract = "We construct an upper bound for the following family of functionals {Eε}ε>0, which arises in the study of micromagnetics: Eε(u)=∫Ωε ∇u 2 + 1/ε ∫ℝ2 Hu 2. Here Ω is a bounded domain in ℝ2, u ∈ H1(Ω, S1) (corresponding to the magnetization) and Hu, the demagnetizing field created by u, is given by Formula is presented, where ũ is the extension of u by 0 in ℝ2\Ω. Our upper bound coincides with the lower bound obtained by Rivi{\`e}re and Serfaty.",

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AB - We construct an upper bound for the following family of functionals {Eε}ε>0, which arises in the study of micromagnetics: Eε(u)=∫Ωε ∇u 2 + 1/ε ∫ℝ2 Hu 2. Here Ω is a bounded domain in ℝ2, u ∈ H1(Ω, S1) (corresponding to the magnetization) and Hu, the demagnetizing field created by u, is given by Formula is presented, where ũ is the extension of u by 0 in ℝ2\Ω. Our upper bound coincides with the lower bound obtained by Rivière and Serfaty.

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Sharp upper bounds for a singular perturbation problem related to micromagnetics

Abstract

ASJC Scopus subject areas

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