Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems

Fuente: arXiv
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Autores principales: Kassymov, Aidyn, Ruzhansky, Michael, Torebek, Berikbol T.
Formato: Preprint
Publicado: 2020
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author Kassymov, Aidyn
Ruzhansky, Michael
Torebek, Berikbol T.
author_facet Kassymov, Aidyn
Ruzhansky, Michael
Torebek, Berikbol T.
contents In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical domains of the same Lebesgue measure. This inequality is called the Rayleigh-Faber-Krahn inequality. Also, we give Lyapunov and Hartmann-Wintner inequalities for the fractional elliptic boundary value problem.
format Preprint
id arxiv_https___arxiv_org_abs_2006_16672
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
Kassymov, Aidyn
Ruzhansky, Michael
Torebek, Berikbol T.
Analysis of PDEs
Spectral Theory
In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical domains of the same Lebesgue measure. This inequality is called the Rayleigh-Faber-Krahn inequality. Also, we give Lyapunov and Hartmann-Wintner inequalities for the fractional elliptic boundary value problem.
title Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
topic Analysis of PDEs
Spectral Theory
url https://arxiv.org/abs/2006.16672