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Pointwise estimate of the solution to a quasilinear elliptic problem in a domain with a thin cavity

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Abstract

We derive a pointwise estimate of the solution to Dirichlet's problem for a quasilinear second-order elliptic equation in a domain whose bounded compliment is contained in a small neighborhood of a set {x ε Rn: ¦x¦ ≤ 1/2, x1=...=xs=0}.

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Literature cited

  1. I. V. Skrypnik, Methods for Studying Nonlinear Elliptic Boundary Value Problems [in Russian], Nauka, Moscow (1990).

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  2. I. V. Skrypnik, “Pointwise estimates of certain capacitative potentials,” in: General Theory of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1983), pp. 198–206.

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  3. I. V. Skrypnik, “Pointwise estimation of the solution to a model nonlinear parabolic problem,” Nelin. Granichn. Zad.,3, 72–86 (1991).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukraine, Donetsk

    I. V. Skrypnik & M. A. Naumova

  2. Donetsk University, USSR

    I. V. Skrypnik & M. A. Naumova

Authors
  1. I. V. Skrypnik
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  2. M. A. Naumova
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1417–1432, October, 1992.

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Skrypnik, I.V., Naumova, M.A. Pointwise estimate of the solution to a quasilinear elliptic problem in a domain with a thin cavity. Ukr Math J 44, 1302–1317 (1992). https://doi.org/10.1007/BF01057690

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  • DOI: https://doi.org/10.1007/BF01057690

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