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math.AP2025
Homogenization of nonlocal exchange energies in micromagnetics
Rossella Giorgio, Leon Happ, Hidde Schönberger
We study the homogenization of nonlocal micromagnetic functionals incorporating both symmetric and antisymmetric exchange contributions under the physical constraint that the magne…
math.AP2025
Nonlocal Micromagnetics: Compactness Criteria, Existence of Minimizers, and Brown's Fundamental Theorem
Giovanni Di Fratta, Rossella Giorgio, Luca Lombardini
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered e…
math.AP2024
A Bourgain-Brezis-Mironescu formula accounting for nonlocal antisymmetric exchange interactions
Elisa Davoli, Giovanni Di Fratta, Rossella Giorgio
The present study concerns the nonlocal-to-local convergence of a family of exchange energy functionals in the limit of very short-range interactions. The analysis accounts for bot…