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A remark on the properties of nonlinear capacity in ℝ3

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Abstract

We consider some relation between the capacities of the three pairs of facets of a 3-dimensional curvilinear hexahedron.

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References

  1. Goldstein V. M. and Reshetnyak Yu. G., Quasiconformal Mappings and Sobolev Spaces, Kluwer, Dordrecht (1983).

    Google Scholar 

  2. Maz’ya V. G., Sobolev Spaces [in Russian], Leningrad Univ., Leningrad (1985).

    Google Scholar 

  3. Evans L. C. and Gariepy R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton (1992).

    MATH  Google Scholar 

  4. Lewis J., “Regularity of the derivatives of solutions to certain elliptic equations,” Indiana Univ. Math. J., 32, No. 6, 849–858 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  5. Romanov A. S., “Capacity relations in a flat quadrilateral,” Siberian Math. J., 49, No. 4, 709–717 (2008).

    Article  MathSciNet  Google Scholar 

  6. Shlyk V. A., “The capacity of a condenser and the modulus of a family of separating surfaces,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 185, 168–182 (1990).

    MATH  Google Scholar 

  7. Dymchenko Yu. V. and Shlyk V. A., “Interrelation between the weighted capacity of a condenser and the weighted modulus of a family of separating surfaces,” Dal’nevostochn. Mat. Sb., No. 2, 72–80 (1996).

  8. Burago Yu. D. and Zalgaller V. A., Geometric Inequalities [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  9. Federer H., Geometric Measure Theory, Springer-Verlag, New York (1969).

    MATH  Google Scholar 

  10. Ziemer W. P., “Extremal length and conformal capacity,” Trans. Amer. Math. Soc., 126, No. 3, 460–473 (1967).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to A. S. Romanov.

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Original Russian Text Copyright © 2012 Romanov A.S.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00662-a) and the Integration Grant of the Siberian Division of the Russian Academy of Sciences, 2009 (No. 30).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 911–919, July–August, 2012.

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Romanov, A.S. A remark on the properties of nonlinear capacity in ℝ3 . Sib Math J 53, 732–738 (2012). https://doi.org/10.1134/S0037446612040143

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