Optimal magnetic Sobolev constants in the semiclassical limit
Analysis of PDEs
2014-11-21 v1
Abstract
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 -norm of the corresponding minimizers near the magnetic wells.
Keywords
Cite
@article{arxiv.1411.5554,
title = {Optimal magnetic Sobolev constants in the semiclassical limit},
author = {Soeren Fournais and Nicolas Raymond},
journal= {arXiv preprint arXiv:1411.5554},
year = {2014}
}