Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian
Analysis of PDEs
2018-08-21 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1603.02810,
title = {Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian},
author = {Soeren Fournais and Loïc Le Treust and Nicolas Raymond and Jean Van Schaftingen},
journal= {arXiv preprint arXiv:1603.02810},
year = {2018}
}