Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

  • Michael Ruzhansky
  • Durvudkhan SuraganEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 216)


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.


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



This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Imperial College LondonLondonUnited Kingdom
  2. 2.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan

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