Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00566027" target="_blank" >RIV/61389005:_____/22:00566027 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/JST/416" target="_blank" >https://doi.org/10.4171/JST/416</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JST/416" target="_blank" >10.4171/JST/416</a>
Alternative languages
Result language
angličtina
Original language name
Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones
Original language description
We consider the problem of geometric optimization of the lowest eigenvalue for the Laplacian on a compact, simply-connected two-dimensional manifold with boundary subject to an attractive Robin boundary condition. We prove that in the sub-class of manifolds with the Gauss curvature bounded from above by a constant K-o >= 0 and under the constraint of fixed perimeter, the geodesic disk of constant curvature K-o maximizes the lowest Robin eigenvalue. In the same geometric setting, it is proved that the spectral isoperimetric inequality holds for the lowest eigenvalue of the Dirichlet-to-Neumann operator. Finally, we adapt our methods to Robin Laplacians acting on unbounded three-dimensional cones to show that, under a constraint of fixed perimeter of the cross-section, the lowest Robin eigenvalue is maximized by the circular cone.
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Spectral Theory
ISSN
1664-039X
e-ISSN
1664-0403
Volume of the periodical
12
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
24
Pages from-to
683-706
UT code for WoS article
000896757900012
EID of the result in the Scopus database
2-s2.0-85140208908