Optimization of the lowest eigenvalue for leaky star graphs

Kód výsledku v 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>
Výsledek na webu
<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>

Jazyk výsledku
angličtina
Název v původním jazyce
Optimization of the lowest eigenvalue for leaky star graphs
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Optimization of the lowest eigenvalue for leaky star graphs
Popis výsledku anglicky
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.

Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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