Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

Michael Ruzhansky; Durvudkhan Suragan

doi:10.1007/978-3-319-67053-9_31

Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of operators on arbitrary domains. We demonstrate these in explicit examples.

Original language	English
Title of host publication	Functional Analysis in Interdisciplinary Applications
Editors	Erlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky
Publisher	Springer New York
Pages	320-329
Number of pages	10
Volume	216
ISBN (Print)	9783319670522
DOIs	https://doi.org/10.1007/978-3-319-67053-9_31
Publication status	Published - Jan 1 2017
Externally published	Yes
Event	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 - Astana, Kazakhstan Duration: Oct 2 2017 → Oct 5 2017

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	216
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
Country/Territory	Kazakhstan
City	Astana
Period	10/2/17 → 10/5/17

Keywords

Geometric extremum problem
Logarithmic potential operator
Luttinger type inequality
Newton potential operator
Polya inequality
Rayleigh-Faber-Krahn inequality
Schatten p-norm

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-67053-9_31

Cite this

Ruzhansky, M., & Suragan, D. (2017). Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. In E. D. Nursultanov, T. S. Kalmenov, M. A. Sadybekov, & M. V. Ruzhansky (Eds.), Functional Analysis in Interdisciplinary Applications (Vol. 216, pp. 320-329). (Springer Proceedings in Mathematics and Statistics; Vol. 216). Springer New York. https://doi.org/10.1007/978-3-319-67053-9_31

Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. / Ruzhansky, Michael; Suragan, Durvudkhan.
Functional Analysis in Interdisciplinary Applications. ed. / Erlan D. Nursultanov; Tynysbek Sh. Kalmenov; Makhmud A. Sadybekov; Michael V. Ruzhansky. Vol. 216 Springer New York, 2017. p. 320-329 (Springer Proceedings in Mathematics and Statistics; Vol. 216).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ruzhansky, M & Suragan, D 2017, Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. in ED Nursultanov, TS Kalmenov, MA Sadybekov & MV Ruzhansky (eds), Functional Analysis in Interdisciplinary Applications. vol. 216, Springer Proceedings in Mathematics and Statistics, vol. 216, Springer New York, pp. 320-329, International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017, Astana, Kazakhstan, 10/2/17. https://doi.org/10.1007/978-3-319-67053-9_31

Ruzhansky, Michael ; Suragan, Durvudkhan. / Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. Functional Analysis in Interdisciplinary Applications. editor / Erlan D. Nursultanov ; Tynysbek Sh. Kalmenov ; Makhmud A. Sadybekov ; Michael V. Ruzhansky. Vol. 216 Springer New York, 2017. pp. 320-329 (Springer Proceedings in Mathematics and Statistics).

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Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

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Keywords

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