Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00575046" target="_blank" >RIV/61389005:_____/23:00575046 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/23:00373044
Result on the web
<a href="https://doi.org/10.1007/s00245-023-10033-1" target="_blank" >https://doi.org/10.1007/s00245-023-10033-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00245-023-10033-1" target="_blank" >10.1007/s00245-023-10033-1</a>

Result language
angličtina
Original language name
Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle
Original language description
We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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