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arXiv · 1603.02810

Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian

Soeren Fournais·Loïc Le Treust·Nicolas Raymond·Jean Van Schaftingen
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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.

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Soeren Fournais, Loïc Le Treust, Nicolas Raymond, Jean Van Schaftingen. 2016-03-09. Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian. https://doi.org/10.2969/jmsj%2F06941667

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