Calculus of Variations and Geometric Measure Theory

G. Di Fratta - C. Muratov - F. Rybakov - V. Slastikov

Variational principles of micromagnetics revisited

created by difratta on 13 May 2019
modified on 30 Apr 2021


Published Paper

Inserted: 13 may 2019
Last Updated: 30 apr 2021

Journal: SIAM Journal on Mathematical Analysis
Volume: 52
Number: 4
Year: 2020


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 non-local. 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: Gamma-convergence, Maxwell's equations, Micromagnetics, Vector magnetic potential, Scalar magnetic potential