Inequalities for the eigenvalues of the Riesz potential

T. Sh Kal’menov; D. Suragan

doi:10.1134/S0001434617110165

Inequalities for the eigenvalues of the Riesz potential

T. Sh Kal’menov, D. Suragan

Research output: Contribution to journal › Article › peer-review

Abstract

It is proved that, of all the domains with identical measure, it is the ball that maximizes the first eigenvalue of the Riesz potential. It is shown that the sum of the squares of all the eigenvalues is also maximized in the ball among all the domains with identical measure.

Original language	English
Pages (from-to)	770-775
Number of pages	6
Journal	Mathematical Notes
Volume	102
Issue number	5-6
DOIs	https://doi.org/10.1134/S0001434617110165
Publication status	Published - Nov 1 2017
Externally published	Yes

Keywords

eigenvalue
Riesz potential
spectral geometry

ASJC Scopus subject areas

General Mathematics

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10.1134/S0001434617110165

Cite this

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abstract = "It is proved that, of all the domains with identical measure, it is the ball that maximizes the first eigenvalue of the Riesz potential. It is shown that the sum of the squares of all the eigenvalues is also maximized in the ball among all the domains with identical measure.",

keywords = "eigenvalue, Riesz potential, spectral geometry",

author = "Kal{\textquoteright}menov, {T. Sh} and D. Suragan",

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AU - Suragan, D.

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PY - 2017/11/1

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N2 - It is proved that, of all the domains with identical measure, it is the ball that maximizes the first eigenvalue of the Riesz potential. It is shown that the sum of the squares of all the eigenvalues is also maximized in the ball among all the domains with identical measure.

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KW - Riesz potential

KW - spectral geometry

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Inequalities for the eigenvalues of the Riesz potential

Abstract

Keywords

ASJC Scopus subject areas

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