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arXiv · 1411.5554

Optimal magnetic Sobolev constants in the semiclassical limit

Soeren Fournais·Nicolas Raymond
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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 $L^\infty$-norm of the corresponding minimizers near the magnetic wells.

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Soeren Fournais, Nicolas Raymond. 2014-11-20. Optimal magnetic Sobolev constants in the semiclassical limit. https://arxiv.org/abs/1411.5554

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