Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00479662" target="_blank" >RIV/61389005:_____/17:00479662 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/17:00312574
Result on the web
<a href="http://dx.doi.org/10.1515/acv-2015-0045" target="_blank" >http://dx.doi.org/10.1515/acv-2015-0045</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/acv-2015-0045" target="_blank" >10.1515/acv-2015-0045</a>
Alternative languages
Result language
angličtina
Original language name
Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
Original language description
We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in two and three dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative).
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Calculus of Variations
ISSN
1864-8258
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
357-379
UT code for WoS article
000411800200003
EID of the result in the Scopus database
2-s2.0-85030701011