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The normal derivative lemma for the Laplacian on a polyhedral set

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Abstract

An analog of the Oleinik-Hopf normal derivative lemma for the Laplace operator on a polyhedral set is considered.

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References

  1. A. A. Gavrilov and O. M. Penkin, “An analogue of the lemma on the normal derivative for an elliptic equation on a stratified set,” Differ. Uravn. 36(2), 226–232 (2000) [Differ. Equations 36 (2), 255–261 (2000)].

    MathSciNet  Google Scholar 

  2. L. S. Pontryagin, Foundations of Combinatorial Topology (Nauka, Moscow, 1986) [in Russian].

    MATH  Google Scholar 

  3. Yu. V. Pokornyi, O.M. Penkin, V. L. Pryadiev, A.V. Borovskikh, K. P. Lazarev, and S.A. Shabrov, Differential Equations on Geometric Graphs (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  4. O. A. Oleinik, “On properties of solutions of certain boundary-value problems for equations of elliptic type,” Mat. Sb. 30(3), 695–702 (1952).

    MathSciNet  Google Scholar 

  5. E. Hopf, “A remark on linear elliptic differential equation of second order,” Proc. Amer. Math. Soc. 3, 791–793 (1952).

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Bers, F. John, and M. Schechter, Partial Differential Equations (Interscience, New York, 1964; Mir, Moscow, 1966).

    MATH  Google Scholar 

  7. S. N. Oshchepkova, O. M. Penkin, and D. V. Savasteev, “Strong maximum principle for an elliptic operator on a stratified set,” Mat. Zametki 92(2), 276–290 (2012) [Math. Notes 92 (2), 249–259 (2012)].

    Article  MathSciNet  Google Scholar 

  8. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer, Berlin, 1983; Nauka, Moscow, 1989).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Belgorod State National Research University, Belgorod, Russia

    S. N. Oshchepkova & O. M. Penkin

  2. Voronezh State University, Voronezh, Russia

    D. V. Savasteev

Authors
  1. S. N. Oshchepkova
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  2. O. M. Penkin
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  3. D. V. Savasteev
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Corresponding author

Correspondence to S. N. Oshchepkova.

Additional information

Original Russian Text © S. N. Oshchepkova, O. M. Penkin, D. V. Savasteev, 2014, published in Matematicheskie Zametki, 2014, Vol. 96, No. 1, pp. 116–125.

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Oshchepkova, S.N., Penkin, O.M. & Savasteev, D.V. The normal derivative lemma for the Laplacian on a polyhedral set. Math Notes 96, 122–129 (2014). https://doi.org/10.1134/S0001434614070116

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  • DOI: https://doi.org/10.1134/S0001434614070116

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