Variational principles of micromagnetics revisited

Giovanni D.I. Fratta, Cyrill B. Muratov, Filipp N. Rybakov, Valeriy V. Slastikov

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3580-3599
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Issue number4
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


  • Maxwell’s equations
  • Micromagnetics
  • Minimizers
  • Stray field
  • Γ-convergence


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