Contemporary Mathematics

0500202 - ÚJF 2019 RIV US eng M - Část monografie knihy
Exner, Pavel - Lotoreichik, Vladimir
Optimization of the lowest eigenvalue for leaky star graphs.
Contemporary Mathematics. Vol. 717. QMATH13. Atlanta: American Mathematical Society, 2018, s. 187-196. ISBN 978-1-4704-3681-0
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: Eigenvalues * mathematical models * Eigenfunctions
Obor OECD: Pure mathematics

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.
Trvalý link: http://hdl.handle.net/11104/0292319