Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian

TY - JOUR

T1 - Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian

AU - Fournais, Søren

AU - Raymond, N.T.

AU - Le Treust, Loïc

AU - van Schaftingen, Jean

PY - 2017

Y1 - 2017

N2 - This paper is devoted to the asymptotic analysis of the optimal Sobolev constants in the semiclassical limit and in any dimension. We combine semiclassical arguments and concentration-compactness estimates to tackle the case when an electro-magnetic field is added as well as a smooth boundary carrying a Robin condition. As a byproduct of the semiclassical strategy, we also get exponentially weighted localization estimates of the minimizers.

AB - This paper is devoted to the asymptotic analysis of the optimal Sobolev constants in the semiclassical limit and in any dimension. We combine semiclassical arguments and concentration-compactness estimates to tackle the case when an electro-magnetic field is added as well as a smooth boundary carrying a Robin condition. As a byproduct of the semiclassical strategy, we also get exponentially weighted localization estimates of the minimizers.

KW - Electromagnetic Laplacian

KW - Robin condition

KW - Semiclassical

KW - Sobolev constants

UR - http://www.scopus.com/inward/record.url?scp=85032801003&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06941667

DO - 10.2969/jmsj/06941667

M3 - Journal article

SN - 0025-5645

VL - 69

SP - 1667

EP - 1714

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 4

ER -