@article{c43ce393875b440dbde5c4d623fc024e,
title = "Variational principles of micromagnetics revisited",
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.",
keywords = "Maxwell{\textquoteright}s equations, Micromagnetics, Minimizers, Stray field, Γ-convergence",
author = "Fratta, {Giovanni D.I.} and Muratov, {Cyrill B.} and Rybakov, {Filipp N.} and Slastikov, {Valeriy V.}",
note = "Funding Information: ∗Received by the editors May 13, 2019; accepted for publication (in revised form) June 22, 2020; published electronically July 30, 2020. https://doi.org/10.1137/19M1261365 Funding: The work of the first author was supported by the Austrian Science Fund (FWF) through the special research program “Taming complexity in partial differential systems” grant SFB F65 and the Vienna Science and Technology Fund (WWTF) through the research project “Thermally controlled magnetization dynamics” grant MA14-44. The work of the second author was partially supported by the National Science Foundation grants DMS-1614948 and DMS-1908709. The work of the third author was supported by the Swedish Research Council grant 642-2013-7837 and the G{\"o}ran Gustafsson Foundation for Research in Natural Sciences and Medicine. The work of the fourth author was supported by the Leverhulme grant RPG-2018-438 and Simons Foundation Fellowship. The work of the first, second and fourth authors was also supported by the Isaac Newton Institute for Mathematical Sciences program “The mathematical design of new materials” supported by EPSRC grants EP/K032208/1 and EP/R014604/1. Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/19M1261365",
language = "English (US)",
volume = "52",
pages = "3580--3599",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}