Quantitative Hardy inequalities for magnetic Hamiltonians

In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators...

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Bibliographic Details
Published in:Communications in partial differential equations 2024-12, Vol.49 (10-12), p.873-891
Main Authors: Fanelli, Luca, Kovařík, Hynek
Format: Article
Language:English
Subjects:
Hardy Inequality
Inequalities
Lower bounds
Magnetic fields
Magnetic flux
magnetic Schrödinger operator
Operators
Pauli operator
Primary: 35R45
Secondary: 47A63
Citations: Items that this one cites
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Summary:In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators with Aharonov-Bohm magnetic field are discussed as well.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2024.2403010