Hardy inequalities for a magnetic Grushin operator with Aharonov–Bohm type magnetic field
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L. Aermark and A. Laptev
Translated by: the authors - St. Petersburg Math. J. 23 (2012), 203-208
- DOI: https://doi.org/10.1090/S1061-0022-2012-01193-3
- Published electronically: January 23, 2012
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Abstract:
A version of the Aharonov–Bohm magnetic field for a Grushin sub-elliptic operator is introduced; then its quadratic form is shown to satisfy an improved Hardy inequality.References
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Bibliographic Information
- L. Aermark
- Affiliation: Stockholm University, SE-106 91 Stockholm, Sweden
- Email: lior@math.su.se
- A. Laptev
- Affiliation: Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
- Email: a.laptev@imperial.ac.uk
- Received by editor(s): November 28, 2010
- Published electronically: January 23, 2012
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 203-208
- MSC (2010): Primary 35P15; Secondary 81Q10
- DOI: https://doi.org/10.1090/S1061-0022-2012-01193-3
- MathSciNet review: 2841670
Dedicated: Dedicated to the memory of M. Sh. Birman whose enormous scientific achievements continue to guide many generations of mathematicians. The strong school in Spectral Theory that he developed is renowned all over the world. All his pupils and colleagues remember Professor Birman as a wonderful person who was always ready to help. His warm and generous support certainly aided the second author of this paper to survive as a mathematician.