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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2008 Volume 83, Issue 1, Pages 3–13 (Mi mzm4334)

This article is cited in 10 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.

UDC: 517.9

Received: 14.07.2006

DOI: 10.4213/mzm4334


 English version:
Mathematical Notes, 2008, 83:1, 3–13

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© Steklov Math. Inst. of RAS, 2025