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Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation

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Abstract

An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.

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Funding

Alkhutov acknowledges the support of the Russian Foundation for Basic Research (project no. 19-01-00184), and Chechkin acknowledges the support of the Russian Science Foundation (project no. 20-11-20272).

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Authors and Affiliations

  1. A.G. and N.G. Stoletovs Vladimir State University, 600000, Vladimir, Russia

    Yu. A. Alkhutov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    G. A. Chechkin

  3. Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, 450000, Ufa, Bashkortostan, Russia

    G. A. Chechkin

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    G. A. Chechkin

Authors
  1. Yu. A. Alkhutov
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  2. G. A. Chechkin
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Corresponding authors

Correspondence to Yu. A. Alkhutov or G. A. Chechkin.

Additional information

Translated by I. Ruzanova

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Alkhutov, Y.A., Chechkin, G.A. Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation. Dokl. Math. 103, 69–71 (2021). https://doi.org/10.1134/S1064562421020022

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  • DOI: https://doi.org/10.1134/S1064562421020022

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