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Harnack’s Inequality for the p(x)-Laplacian with a Two-Phase Exponent p(x)

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Abstract

One considers solutions of the p(x)-Laplacian equation in a neighborhood of a point x0 on a hyperplane Σ. It is assumed that the exponent p(x) possesses a logarithmic continuity modulus as x0 is approached from one of the half-spaces separated by Σ. A version of the Harnack inequality is proved for these solutions.

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Author information

Authors and Affiliations

  1. Vladimir State Humanitarian University, Vladimir, Russia

    Yu. A. Alkhutov

  2. Moscow State University, Moscow, Russia

    M. D. Surnachev

Authors
  1. Yu. A. Alkhutov
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  2. M. D. Surnachev
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Corresponding author

Correspondence to Yu. A. Alkhutov.

Additional information

Dedicated to the memory of Vasilii Vasilievich Zhikov

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 32, pp. 8–56, 2019.

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Alkhutov, Y.A., Surnachev, M.D. Harnack’s Inequality for the p(x)-Laplacian with a Two-Phase Exponent p(x). J Math Sci 244, 116–147 (2020). https://doi.org/10.1007/s10958-019-04609-y

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  • DOI: https://doi.org/10.1007/s10958-019-04609-y

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