# Variational principles of micromagnetics revisited

## TL;DR

This paper revisits the fundamental variational principles in micromagnetics, focusing on the non-local stray field energy and deriving new formulations applicable to thin ferromagnetic shells.

## Contribution

It introduces three new variational principles for the stray field energy, enhancing understanding and computational approaches in micromagnetics.

## Key findings

- Established three variational principles for stray field energy
- Applied formulations to thin ferromagnetic shells
- Provided a rigorous mathematical framework for non-local energy contributions

## 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 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.