The first Robin eigenvalue with negative boundary parameter

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F15%3A00446668" target="_blank" >RIV/61389005:_____/15:00446668 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2015.04.023" target="_blank" >http://dx.doi.org/10.1016/j.aim.2015.04.023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2015.04.023" target="_blank" >10.1016/j.aim.2015.04.023</a>

Result language
angličtina
Original language name
The first Robin eigenvalue with negative boundary parameter
Original language description
We give a counterexample to the long standing conjecture that the ball maximises the first eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the same volume. Furthermore, we show that the conjecture holds in two dimensions provided that the boundary parameter is small. This is the first known example within the class of isoperimetric spectral problems for the first eigenvalue of the Laplacian where the ball is not an optimiser.
Czech name
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Czech description
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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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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

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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