Inequalities for the eigenvalues of the Riesz potential

Inequalities for the eigenvalues of the Riesz potential

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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Bibliographische Detailangaben
Veröffentlicht in:Mathematical Notes 2017-11, Vol.102 (5-6), p.770-775
Hauptverfasser: Kal’menov, T. Sh, Suragan, D.
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434617110165