Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

Michael Ruzhansky, Durvudkhan Suragan

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationFunctional Analysis in Interdisciplinary Applications
EditorsErlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky
PublisherSpringer New York
Pages320-329
Number of pages10
Volume216
ISBN (Print)9783319670522
DOIs
Publication statusPublished - Jan 1 2017
Externally publishedYes
EventInternational Conference on Functional analysis in interdisciplinary applications, FAIA 2017 - Astana, Kazakhstan
Duration: Oct 2 2017Oct 5 2017

Conference

ConferenceInternational Conference on Functional analysis in interdisciplinary applications, FAIA 2017
CountryKazakhstan
CityAstana
Period10/2/1710/5/17

Fingerprint

Isoperimetric Inequality
Potential Theory
Integral Operator
Extremum Problem
Logarithmic Potential
Potential Operators
Isoperimetric
A Priori Bounds
Invariant
Arbitrary
Operator
Demonstrate
Review

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

  • Mathematics(all)

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 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.

Research output: Chapter in Book/Report/Conference proceedingConference 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 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 M, Suragan D. Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. In Nursultanov ED, Kalmenov TS, Sadybekov MA, Ruzhansky MV, editors, Functional Analysis in Interdisciplinary Applications. Vol. 216. Springer New York. 2017. p. 320-329 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
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