Optimization of the lowest eigenvalue for leaky star graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00500202" target="_blank" >RIV/61389005:_____/18:00500202 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/conm/717/14448" target="_blank" >http://dx.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>

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-imensional Schrödinger operator with an attractive delta-interaction of a fixed strength, the support of which is a star graph with finitely many edges of an equal length is in the interval from 0 to 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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Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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