Optimal magnetic Sobolev constants in the semiclassical limit

TY - JOUR

T1 - Optimal magnetic Sobolev constants in the semiclassical limit

AU - Fournais, S.

AU - Raymond, N.T.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - CALCULUS

KW - CONCENTRATION-COMPACTNESS PRINCIPLE

KW - ENERGY

KW - FIELDS

KW - Magnetic

KW - NONLINEAR SCHRODINGER-EQUATIONS

KW - Nonlinear Schrodinger equation

KW - OPERATORS

KW - STATES

KW - Semiclassical

KW - WELLS

UR - http://www.scopus.com/inward/record.url?scp=84929095089&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2015.03.008

DO - 10.1016/j.anihpc.2015.03.008

M3 - Journal article

SN - 0294-1449

VL - 33

SP - 1199

EP - 1222

JO - Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire

JF - Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire

IS - 5

ER -