The Hardy inequality and the heat equation with magnetic field in any dimension
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00462436" target="_blank" >RIV/61389005:_____/16:00462436 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/03605302.2016.1179317" target="_blank" >http://dx.doi.org/10.1080/03605302.2016.1179317</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03605302.2016.1179317" target="_blank" >10.1080/03605302.2016.1179317</a>
Alternative languages
Result language
angličtina
Original language name
The Hardy inequality and the heat equation with magnetic field in any dimension
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Partial Differential Equations
ISSN
0360-5302
e-ISSN
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Volume of the periodical
41
Issue of the periodical within the volume
7
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
1056-1088
UT code for WoS article
000380142200003
EID of the result in the Scopus database
2-s2.0-84975282623