An isoperimetric inequality for the perturbed Robin bi-Laplacian in 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_____%2F23%3A00566557" target="_blank" >RIV/61389005:_____/23:00566557 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jde.2022.11.016" target="_blank" >https://doi.org/10.1016/j.jde.2022.11.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2022.11.016" target="_blank" >10.1016/j.jde.2022.11.016</a>
Alternative languages
Result language
angličtina
Original language name
An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain
Original language description
We introduce the perturbed two-dimensional Robin bi-Laplacian in the exterior of a planar bounded simply-connected C2-smooth open set. The considered lower-order perturbation corresponds to tension. We prove that the essential spectrum of this operator coincides with the positive semi-axis and that the negative discrete spectrum is non-empty if the boundary parameter is negative. As the main result, we obtain an isoperimetric inequality for the lowest eigenvalue of such a perturbed Robin bi-Laplacian with a negative boundary parameter in the exterior of a bounded convex planar set under the constraint on the maximum of the curvature of the boundary with the maximizer being the exterior of the disk. The isoperimetric inequality is proved under the assumption that to the lowest eigenvalue for the exterior of the disk corresponds a radial eigenfunction. We provide a sufficient condition in terms of the tension parameter and the radius for this property to hold.
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/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
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 Differential Equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
345
Issue of the periodical within the volume
FEB
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
285-313
UT code for WoS article
000897817400009
EID of the result in the Scopus database
2-s2.0-85142725736