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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 278, Pages 7–15 (Mi tm3407)  
This article is cited in 10 scientific papers (total in 10 papers)

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

Yu. A. Alkhutov, E. A. Khrenova

Vladimir State University, Vladimir, Russia
Full-text PDF (177 kB) Citations (10)
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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.
Received in May 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 278, Pages 1–9
DOI: https://doi.org/10.1134/S0081543812060016
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: Yu. A. Alkhutov, E. A. Khrenova, “Harnack inequality for a class of second-order degenerate elliptic equations”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 7–15; Proc. Steklov Inst. Math., 278 (2012), 1–9
Citation in format AMSBIB
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\pages 7--15
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://www.mathnet.ru/eng/tm/v278/p7
    • This publication is cited in the following 10 articles:
    1. Yanli Wang, Xianghong Li, Yongjun Shen, “Study on Mechanical Vibration Control of Limit Cycle Oscillations in the Van der Pol Oscillator by means of Nonlinear Energy Sink”, J. Vib. Eng. Technol., 12:1 (2024), 811  crossref
    2. M. J. Aliyev, Yu. A. Alkhutov, R. N. Tikhomirov, “Harnack Inequality for Elliptic (p, q)-Laplacian with Partially Muckenhoupt Weight”, J Math Sci, 262:3 (2022), 233  crossref
    3. Yu. A. Alkhutov, M. D. Surnachev, “The Boundary Behavior of a Solution to the Dirichlet Problem for a Linear Degenerate Second Order Elliptic Equation”, J Math Sci, 259:2 (2021), 109  crossref
    4. Yu. A. Alkhutov, M. D. Surnachev, “The Boundary Behavior of a Solution to the Dirichlet Problem for the p-Laplacian with Weight Uniformly Degenerate on a Part of Domain with Respect to Small Parameter”, J Math Sci, 250:2 (2020), 183  crossref
    5. Alkhutov Yu.A., Huseynov S.T., “Holder Continuity of Solutions of An Elliptic P(X)-Laplace Equation Uniformly Degenerate on a Part of the Domain”, Differ. Equ., 55:8 (2019), 1056–1068  crossref  mathscinet  isi  scopus
    6. Yu. A. Alkhutov, S. T. Huseynov, “Harnack's inequality for p-Laplacian equations with Muckenhoupt weight degenerating in part of the domain”, Electron. J. Differ. Equ., 2017, 79  mathscinet  zmath  isi
    7. S. T. Huseynov, “Harnack inequality for the solutions of the p-Laplacian with a partially Muckenhoupt weight”, Differ. Equ., 53:5 (2017), 646–657  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    8. Yu. A. Alkhutov, M. D. Surnachev, “On a Harnack inequality for the elliptic (p,q)-Laplacian”, Dokl. Math., 94:2 (2016), 569–573  crossref  mathscinet  zmath  isi  elib  scopus
    9. M. D. Surnachev, “Hölder Continuity of Solutions to Nonlinear Parabolic Equations Degenerated on a Part of the Domain”, J Math Sci, 213:4 (2016), 610  crossref
    10. M. D. Surnachev, “On the Hölder continuity of solutions to nonlinear parabolic equations degenerating on part of the domain”, Dokl. Math., 92:1 (2015), 412–416  crossref  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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