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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 3–13 (Mi mz4334)  

This article is cited in 2 scientific papers (total in 2 papers)

Regularity of the Solutions of Degenerate Elliptic Equations in Divergent Form

R. A. Amanova, F. I. Mamedovb

a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
b Dicle University

Abstract: A priori estimates of the solution to the Dirichlet problem and of its first derivatives in terms of weighted Lebesgue norms are obtained for linear and quasilinear equations with degeneracy from $A_p$ Muckenhoupt classes.

Keywords: elliptic equation of divergence form, Dirichlet problem, Lipschitz condition, Lebesgue norm, Lebesgue measure, Hölder's inequality

DOI: https://doi.org/10.4213/mzm4334

Full text: PDF file (480 kB)
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English version:
Mathematical Notes, 2008, 83:1, 3–13

Bibliographic databases:

UDC: 517.9
Received: 14.07.2006

Citation: R. A. Amanov, F. I. Mamedov, “Regularity of the Solutions of Degenerate Elliptic Equations in Divergent Form”, Mat. Zametki, 83:1 (2008), 3–13; Math. Notes, 83:1 (2008), 3–13

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mamedov F.I., Ibragimov T.T., “On the behavior of solutions of some nonlinear degenerate elliptic inequalities”, Differ. Equ., 46:5 (2010), 711–721  crossref  mathscinet  zmath  isi  isi  elib  scopus
    2. Mamedov F., Shukurov Ya., “A Sawyer-Type Sufficient Condition For the Weighted Poincaré, Inequality”, Positivity, 22:3 (2018), 687–699  crossref  mathscinet  isi  scopus
  • Математические заметки Mathematical Notes
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