Optimisation and monotonicity of the second Robin eigenvalue on a planar exterior domain
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00599312" target="_blank" >RIV/61389005:_____/24:00599312 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00526-024-02824-3" target="_blank" >https://doi.org/10.1007/s00526-024-02824-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-024-02824-3" target="_blank" >10.1007/s00526-024-02824-3</a>
Alternative languages
Result language
angličtina
Original language name
Optimisation and monotonicity of the second Robin eigenvalue on a planar exterior domain
Original language description
We consider the Laplace operator in the exterior of a compact set in the plane, subject to Robin boundary conditions. If the boundary coupling is sufficiently negative, there are at least two discrete eigenvalues below the essential spectrum. We state a general conjecture that the second eigenvalue is maximised by the exterior of a disk under isochoric or isoperimetric constraints. We prove an isoelastic version of the conjecture for the exterior of convex domains. Finally, we establish a monotonicity result for the second eigenvalue under the condition that the compact set is strictly star-shaped and centrally symmetric.
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
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
1432-0835
Volume of the periodical
63
Issue of the periodical within the volume
9
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
223
UT code for WoS article
001325837900002
EID of the result in the Scopus database
2-s2.0-85205671975