Optimization of the lowest eigenvalue for leaky star graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00346535" target="_blank" >RIV/68407700:21340/18:00346535 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/conm/717/14448" target="_blank" >https://doi.org/10.1090/conm/717/14448</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/conm/717/14448" target="_blank" >10.1090/conm/717/14448</a>
Alternative languages
Result language
angličtina
Original language name
Optimization of the lowest eigenvalue for leaky star graphs
Original language description
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schriidinger operator with an attractive (5 interaction of a fixed strength, the support of which is a star graph with finitely many edges of an equal length L is an element of (0, infinity]. Under the constraint of fixed number of the edges and fixed length of them, we prove that the lowest eigenvalue is maximized by the fully symmetric star graph. The proof relies on the Birman-Schwinger principle, properties of the Macdonald function, and on a geometric inequality for polygons circumscribed into the unit circle.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
MATHEMATICAL PROBLEMS IN QUANTUM PHYSICS
ISBN
978-1-4704-3681-0
ISSN
0271-4132
e-ISSN
1098-3627
Number of pages
10
Pages from-to
187-196
Publisher name
American Mathematical Society
Place of publication
Providence
Event location
Georgia Inst Technol, Atlanta, GA
Event date
Oct 8, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000465195200012