Variational principles of micromagnetics revisited

Document Type

Article

Publication Date

1-1-2020

Abstract

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 nonlocal. 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.

Identifier

85086828657 (Scopus)

Publication Title

SIAM Journal on Mathematical Analysis

External Full Text Location

https://doi.org/10.1137/19M1261365

e-ISSN

10957154

ISSN

00361410

First Page

3580

Last Page

3599

Issue

4

Volume

52

Grant

EP/K032208/1

Fund Ref

Isaac Newton Institute for Mathematical Sciences

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