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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…
Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory
Elisa Davoli, Leon Happ
In this paper we prove a strong two-scale approximation result for sphere-valued maps in , where is an open domain and $…
On the existence of extensions for manifold-valued Sobolev maps on perforated domains
Chiara Gavioli, Leon Happ, Valerio Pagliari
Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, con…
A modular Poincaré-Wirtinger type inequality on Lipschitz domains for Sobolev spaces with variable exponents
Elisa Davoli, Giovanni Di Fratta, Alberto Fiorenza +1
In the context of Sobolev spaces with variable exponents, Poincaré--Wirtinger inequalities are possible as soon as Luxemburg norms are considered. On the other hand, modular versio…