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Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

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Functional Analysis in Interdisciplinary Applications (FAIA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

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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.

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Acknowledgements

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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Authors and Affiliations

  1. Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom

    Michael Ruzhansky

  2. Institute of Mathematics and Mathematical Modeling, 125 Pushkin st., Almaty, 050010, Kazakhstan

    Durvudkhan Suragan

Authors
  1. Michael Ruzhansky
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  2. Durvudkhan Suragan
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Corresponding author

Correspondence to Durvudkhan Suragan .

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Ruzhansky, M., Suragan, D. (2017). Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_31

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