Imperial College London
Professor Ari Laptev

ProfessorAriLaptev

Faculty of Natural Sciences, Department of Mathematics

Chair in Pure Mathematics
 
 
 
//

Contact

 

+44 (0)20 7594 8499a.laptev Website

 
 
//

Assistant

 

Mr David Whittaker +44 (0)20 7594 8481

 
//

Location

 

680Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Bonheure:2020:10.1007/s00220-019-03560-y,
author = {Bonheure, D and Dolbeault, J and Esteban, MJ and Laptev, A and Loss, M},
doi = {10.1007/s00220-019-03560-y},
journal = {Communications in Mathematical Physics},
pages = {2071--2087},
title = {Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields},
url = {http://dx.doi.org/10.1007/s00220-019-03560-y},
volume = {375},
year = {2020}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov–Bohm magnetic vector potential. We investigate the symmetry properties of the optimal potential for the corresponding magnetic Keller–Lieb–Thirring inequality. We prove that this potential is radially symmetric if the intensity of the magnetic field is below an explicit threshold, while symmetry is broken above a second threshold corresponding to a higher magnetic field. The method relies on the study of the magnetic kinetic energy of the wave function and amounts to study the symmetry properties of the optimal functions in a magnetic Hardy–Sobolev interpolation inequality. We give a quantified range of symmetry by a non-perturbative method. To establish the symmetry breaking range, we exploit the coupling of the phase and of the modulus and also obtain a quantitative result.
AU  - Bonheure,D
AU  - Dolbeault,J
AU  - Esteban,MJ
AU  - Laptev,A
AU  - Loss,M
DO  - 10.1007/s00220-019-03560-y
EP  - 2087
PY  - 2020///
SN  - 0010-3616
SP  - 2071
TI  - Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields
T2  - Communications in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s00220-019-03560-y
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000529280100013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00220-019-03560-y
UR  - http://hdl.handle.net/10044/1/79353
VL  - 375
ER  -
Download