Optimal magnetic Sobolev constants in the semiclassical limit

  • S. Fournais

    Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
  • N. Raymond

    IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex, France

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.

Cite this article

S. Fournais, N. Raymond, Optimal magnetic Sobolev constants in the semiclassical limit. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 5, pp. 1199–1222

DOI 10.1016/J.ANIHPC.2015.03.008