We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of R-2 endowed with an Aharonov-Bohm potential. When the flux of the potential around the pole is not an integer, the lowest eigenvalue for the Neumann and the Steklov problems is positive. We establish isoperimetric inequalities for the lowest eigenvalue in the spirit of the classical inequalities of Szego-Weinberger, Brock and Weinstock, the model domain being a disk with the pole at its center. We consider more generally domains in the plane endowed with a rotationally invariant metric, which include the spherical and the hyperbolic case.

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential / Colbois, Bruno; Provenzano, Luigi; Savo, Alessandro. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:11(2022). [10.1007/s12220-022-01001-2]

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential

Luigi Provenzano
;
Alessandro Savo
2022

Abstract

We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of R-2 endowed with an Aharonov-Bohm potential. When the flux of the potential around the pole is not an integer, the lowest eigenvalue for the Neumann and the Steklov problems is positive. We establish isoperimetric inequalities for the lowest eigenvalue in the spirit of the classical inequalities of Szego-Weinberger, Brock and Weinstock, the model domain being a disk with the pole at its center. We consider more generally domains in the plane endowed with a rotationally invariant metric, which include the spherical and the hyperbolic case.
2022
Magnetic Laplacian; Aharonov-Bohm magnetic potential; Ground state; Neumann problem; Steklov problem; Reverse Faber-Krahn inequality
01 Pubblicazione su rivista::01a Articolo in rivista
Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential / Colbois, Bruno; Provenzano, Luigi; Savo, Alessandro. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:11(2022). [10.1007/s12220-022-01001-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654923
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