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Inequalities for the lowest magnetic Neumann eigenvalue

  • S. FournaisEmail author
  • B. Helffer
Article
  • 16 Downloads

Abstract

We study the ground-state energy of the Neumann magnetic Laplacian on planar domains. For a constant magnetic field, we consider the question whether the disc maximizes this eigenvalue for fixed area. More generally, we discuss old and new bounds obtained on this problem.

Keywords

Spectral theory Isoperimetric inequalities Magnetic Faber-Krahn inequality 

Mathematics Subject Classification

35P15 

Notes

Acknowledgements

The discussion on this problem started at a nice meeting in Oberwolfach (December 2014) organized by Bonnaillie–Noël, Kovařík and Pankrashkin. We would like to thank M. van den Berg, D. Bucur, B. Colbois, M. Persson Sundqvist, K. Pankrashkin, N. Popoff and A. Savo for discussions around this problem. We also thank the referee for additional references.

Funding

Funding was provided by Det Frie Forskningsråd (Grant No. DFF-4181-00221).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Aarhus UniversityAarhus CDenmark
  2. 2.LMJLUniversité de Nantes and CNRSNantes CedexFrance

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