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On the modulus of continuity of the solution to the Dirichlet problem at a regular boundary point

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Abstract

A linear elliptic equation of second order with coefficients satisfying a Dini condition is considered in the paper. The modulus of continuity of a solution at a regular boundary point is investigated. An estimate for the modulus of continuity in terms of the Wiener capacity is obtained.

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Literature cited

  1. V. G. Maz'ya, “On the modulus of continuity of a solution of the Dirichlet problem near a nonregular boundary,” in: Problems of Mathematical Analysis [in Russian], Leningrad (1966), pp. 45–58.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. A. Novruzov

Authors
  1. A. A. Novruzov
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Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 67–72, July, 1972.

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Novruzov, A.A. On the modulus of continuity of the solution to the Dirichlet problem at a regular boundary point. Mathematical Notes of the Academy of Sciences of the USSR 12, 472–475 (1972). https://doi.org/10.1007/BF01094394

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  • DOI: https://doi.org/10.1007/BF01094394

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