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Harnack inequality for a class of second-order degenerate elliptic equations

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Abstract

A second-order degenerate elliptic equation in divergence form with a partially Muckenhoupt weight is studied. In a model case, the domain is divided by a hyperplane into two parts, and in each part the weight is a power function of |x| with the exponent less than the dimension of the space in absolute value. It is well known that solutions of such equations are Hölder continuous, whereas the classical Harnack inequality is missing. In this paper, we formulate and prove the Harnack inequality corresponding to the second-order degenerate elliptic equation under consideration.

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Authors and Affiliations

  1. Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia

    Yu. A. Alkhutov & E. A. Khrenova

Authors
  1. Yu. A. Alkhutov
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  2. E. A. Khrenova
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Correspondence to Yu. A. Alkhutov.

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Original Russian Text © Yu.A. Alkhutov, E.A. Khrenova, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 278, pp. 7–15.

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Alkhutov, Y.A., Khrenova, E.A. Harnack inequality for a class of second-order degenerate elliptic equations. Proc. Steklov Inst. Math. 278, 1–9 (2012). https://doi.org/10.1134/S0081543812060016

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  • DOI: https://doi.org/10.1134/S0081543812060016

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