An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-07129S" target="_blank" >GA21-07129S: Nové jevy pocházející z narušení invariance vůči časové inversi</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

345

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

285-313

Kód UT WoS článku

000897817400009

EID výsledku v databázi Scopus

2-s2.0-85142725736