Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian
  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 electromagnetic 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. 
Soeren Fournais (University of Aarhus), Lo\"ic Le Treust (IPSO,   IRMAR), Nicolas Raymond (IRMAR), Jean Van Schaftingen
math.AP