Strong diamagnetism for general domains and application

Soeren Fournais[1]; Bernard Helffer[2]

  • [1] Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France) and University of Aarhus Department of Mathematical Sciences Ny Munkegade, Building 1530 8000 Aarhus C (Denmark)
  • [2] Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 7, page 2389-2400
  • ISSN: 0373-0956

Abstract

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We consider the Neumann Laplacian with constant magnetic field on a regular domain in ℝ 2 . Let B be the strength of the magnetic field and let λ 1 ( B ) be the first eigenvalue of this Laplacian. It is proved that B ↦ λ 1 ( B ) is monotone increasing for large B . Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

How to cite

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Fournais, Soeren, and Helffer, Bernard. "Strong diamagnetism for general domains and application." Annales de l’institut Fourier 57.7 (2007): 2389-2400. <http://eudml.org/doc/10301>.

@article{Fournais2007,
abstract = {We consider the Neumann Laplacian with constant magnetic field on a regular domain in $\mathbb\{R\}^2$. Let $B$ be the strength of the magnetic field and let $\lambda _1(B)$ be the first eigenvalue of this Laplacian. It is proved that $B \mapsto \lambda _1(B)$ is monotone increasing for large $B$. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.},
affiliation = {Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France) and University of Aarhus Department of Mathematical Sciences Ny Munkegade, Building 1530 8000 Aarhus C (Denmark); Université Paris-Sud Laboratoire de Mathématiques UMR CNRS 8628 Bât 425 91405 Orsay Cedex (France)},
author = {Fournais, Soeren, Helffer, Bernard},
journal = {Annales de l’institut Fourier},
keywords = {Spectral theory; bottom of the spectrum; Neumann condition; superconductivity; spectral theory},
language = {eng},
number = {7},
pages = {2389-2400},
publisher = {Association des Annales de l’institut Fourier},
title = {Strong diamagnetism for general domains and application},
url = {http://eudml.org/doc/10301},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Fournais, Soeren
AU - Helffer, Bernard
TI - Strong diamagnetism for general domains and application
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 7
SP - 2389
EP - 2400
AB - We consider the Neumann Laplacian with constant magnetic field on a regular domain in $\mathbb{R}^2$. Let $B$ be the strength of the magnetic field and let $\lambda _1(B)$ be the first eigenvalue of this Laplacian. It is proved that $B \mapsto \lambda _1(B)$ is monotone increasing for large $B$. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.
LA - eng
KW - Spectral theory; bottom of the spectrum; Neumann condition; superconductivity; spectral theory
UR - http://eudml.org/doc/10301
ER -

References

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