Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-01706S" target="_blank" >GA17-01706S: Matematicko-fyzikální modely nových materiálů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Spectral Theory

ISSN

1664-039X

e-ISSN

1664-0403

Svazek periodika

12

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

683-706

Kód UT WoS článku

000896757900012

EID výsledku v databázi Scopus

2-s2.0-85140208908