R. A. Amanov, F. I. Mamedov, “Regularity of the Solutions of Degenerate Elliptic Equations in Divergent Form”, Mat. Zametki, 2008, Volume 83, Issue 1,Pages <nobr>3

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Regularity of the Solutions of Degenerate Elliptic Equations in Divergent Form

R. A. Amanov^a, F. I. Mamedov^b

^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