Počet záznamů: 1
The Hardy inequality and the heat equation with magnetic field in any dimension
- 1.
SYSNO ASEP 0462436 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název The Hardy inequality and the heat equation with magnetic field in any dimension Tvůrce(i) Cazacu, C. (RO)
Krejčiřík, David (UJF-V) RIDCelkový počet autorů 2 Zdroj.dok. Communications in Partial Differential Equations. - : Taylor & Francis - ISSN 0360-5302
Roč. 41, č. 7 (2016), s. 1056-1088Poč.str. 33 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Aharonov-Bohm magnetic field ; Hardy inequality ; heat equation ; large time behaviour of solutions ; magnetic Schrodinger operator Vědní obor RIV BE - Teoretická fyzika CEP GA14-06818S GA ČR - Grantová agentura ČR Institucionální podpora UJF-V - RVO:61389005 UT WOS 000380142200003 EID SCOPUS 84975282623 DOI 10.1080/03605302.2016.1179317 Anotace n the Euclidean space of any dimension d, we consider the heat semi group generated by the magnetic Schrodinger operator from which an inverse-square potential is subtracted to make the operator critical in the magnetic-free case. Assuming that the magnetic field is compactly supported, we show that the polynomial large-time behavior of the heat semigroup is determined by the eigenvalue problem for a magnetic Schrodinger operator on the (d-1)-dimensional sphere whose vector potential reflects the behavior of the magnetic field at the space infinity. From the spectral problem on the sphere, we deduce that in d = 2 there is an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta, while there is no extra polynomial decay rate in higher dimensions. To prove the results, we establish new magnetic Hardy-type inequalities for the Schrodinger operator and develop the method of self-similar variables and weighted Sobolev spaces for the associated heat equation. Pracoviště Ústav jaderné fyziky Kontakt Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Rok sběru 2017
Počet záznamů: 1