Geodesic
Optimal magnetic Sobolev constants in the semiclassical limit
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1199-1222

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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∞-norm of the corresponding minimizers near the magnetic wells.

DOI : 10.1016/j.anihpc.2015.03.008
Keywords: Nonlinear Schrödinger equation, Semiclassical, Magnetic 
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     title = {Optimal magnetic {Sobolev} constants in the semiclassical limit},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1199--1222},
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Fournais, S.; Raymond, N. Optimal magnetic Sobolev constants in the semiclassical limit. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 5, pp. 1199-1222. doi: 10.1016/j.anihpc.2015.03.008

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