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The Meyers Estimates for Domains Perforated along the Boundary

Author

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  • Gregory A. Chechkin

    (Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Leninskie Gory, 1, 119991 Moscow, Russia
    Institute of Mathematics with Computing Center, Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Chernyshevskogo st., 112, 450008 Ufa, Russia
    Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty 050010, Kazakhstan)

Abstract

In this paper, we consider an elliptic problem in a domain perforated along the boundary. By setting a homogeneous Dirichlet condition on the boundary of the cavities and a homogeneous Neumann condition on the outer boundary of the domain, we prove higher integrability of the gradient of the solution to the problem.

Suggested Citation

  • Gregory A. Chechkin, 2021. "The Meyers Estimates for Domains Perforated along the Boundary," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3015-:d:687175
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    References listed on IDEAS

    as
    1. G. A. Chechkin & Yu. O. Koroleva & L.-E. Persson & P. Wall, 2011. "On Spectrum of the Laplacian in a Circle Perforated along the Boundary: Application to a Friedrichs-Type Inequality," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-22, November.
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    Cited by:

    1. Kuanysh A. Bekmaganbetov & Gregory A. Chechkin & Vladimir V. Chepyzhov, 2023. "Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles," Mathematics, MDPI, vol. 11(6), pages 1-21, March.

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