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Zap. Nauchn. Sem. POMI, 2016, Volume 449, Pages 196–213 (Mi znsl6327)  

This article is cited in 1 scientific paper (total in 1 paper)

On the $p$-harmonic Robin radius in the Euclidean space

S. I. Kalmykovab, E. G. Prilepkinacd

a Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan RD, Shanghai, 200240, China
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia
c Far Eastern Federal University, Vladivostok, Russia
d Vladivostok Branch of Russian Customs Academy, Vladivostok, Russia

Abstract: For $p>1$, the notion of the $p$-harmonic Robin radius is introduced in the space $\mathbb R^n$, $n\geq2$. If the corresponding part of the boundary degenerates the Robin–Neumann radius is considered. The monotonicity of the $p$-harmonic Robin radius under some deformations of a domain is proved. In the Euclidean space, some extremal decomposition problems are solved. The definitions and proofs are based on the technique of modules of curve families.

Key words and phrases: $p$-harmonic function, Robin radius, condencer capacity, module of curve family, extremal decomposition.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022


Full text: PDF file (245 kB)
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English version:
Journal of Mathematical Sciences (New York), 2017, 225:6, 969–979

Bibliographic databases:

UDC: 517.5
Received: 19.08.2016

Citation: S. I. Kalmykov, E. G. Prilepkina, “On the $p$-harmonic Robin radius in the Euclidean space”, Analytical theory of numbers and theory of functions. Part 32, Zap. Nauchn. Sem. POMI, 449, POMI, St. Petersburg, 2016, 196–213; J. Math. Sci. (N. Y.), 225:6 (2017), 969–979

Citation in format AMSBIB
\Bibitem{KalPri16}
\by S.~I.~Kalmykov, E.~G.~Prilepkina
\paper On the $p$-harmonic Robin radius in the Euclidean space
\inbook Analytical theory of numbers and theory of functions. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 449
\pages 196--213
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6327}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3580136}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 6
\pages 969--979
\crossref{https://doi.org/10.1007/s10958-017-3508-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85027339133}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. G. Prilepkina, “O $n$-garmonicheskom radiuse oblastei v $n$-mernom evklidovom prostranstve”, Dalnevost. matem. zhurn., 17:2 (2017), 246–256  mathnet  elib
  • Записки научных семинаров ПОМИ
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