Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian

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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Cited by in corpus (3)

• On the fractional Schrödinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity
• Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field
• On the bound states of magnetic Laplacians on wedges