A spectral isoperimetric inequality for cones

0474568 - ÚJF 2018 RIV NL eng J - Článek v odborném periodiku
Exner, Pavel - Lotoreichik, Vladimir
A spectral isoperimetric inequality for cones.
Letters in Mathematical Physics. Roč. 107, č. 4 (2017), s. 717-732. ISSN 0377-9017. E-ISSN 1573-0530
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: Shrodinger operator * delta-interaction * conical surface * isoperimetric inequality * existence of bound states
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 1.306, rok: 2017

In this note, we investigate three-dimensional Schrodinger operators with delta-interactions supported on C-2-smooth cones, both finite and infinite. Our main results concern a Faber-Krahn-type inequality for the principal eigenvalue of these operators. The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimizers for a class of energy functionals. The main novel idea consists in the way of constructing test functions for the Birman-Schwinger principle.
Trvalý link: http://hdl.handle.net/11104/0271590