Optimal magnetic Sobolev constants in the semiclassical limit
Résumé
This paper is devoted to the semiclassical analysis of the best constants in the magnetic Sobolev embeddings in the case of a bounded domain of the plane carrying Dirichlet conditions. We provide quantitative estimates of these constants (with an explicit dependence on the semiclassical parameter) and analyze the exponential localization in $L^{\infty}$-norm of the corresponding minimizers near the magnetic wells.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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