Calculus of Variations and Geometric Measure Theory
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H. Kovarik

Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

created by kovarik on 29 Aug 2011
modified on 28 Apr 2015

[BibTeX]

Published Paper

Inserted: 29 aug 2011
Last Updated: 28 apr 2015

Journal: J. Spectr. Theory
Volume: 1
Number: 4
Pages: 363-387
Year: 2011

Abstract:

We prove that the number of negative eigenvalues of two-dimensional magnetic Schrödinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We also show how the corresponding upper bounds depend on the properties of the magnetic field and discuss their connection with Hardy-type inequalities.


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