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

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Matematicheskie Zametki, 2008, Volume 83, Issue 1, Pages 3–13
DOI: https://doi.org/10.4213/mzm4334 (Mi mzm4334)

This article is cited in 10 scientific papers (total in 10 papers)

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

Full-text PDF (480 kB) Citations (10)

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

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.

Received: 14.07.2006

English version:
Mathematical Notes, 2008, Volume 83, Issue 1, Pages 3–13
DOI: https://doi.org/10.1134/S000143460801001X

Bibliographic databases:

UDC: 517.9

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/mzm4334

https://doi.org/10.4213/mzm4334

https://www.mathnet.ru/eng/mzm/v83/i1/p3

This publication is cited in the following 10 articles:

Giuseppe Di Fazio, Farman Mamedov, “On Harnack inequality and Hölder continuity for non uniformly elliptic equations”, Ricerche mat, 2024
F. Mamedov, G. Gasymov, “Positive Solutions of Nonuniformly Elliptic Equations with Weighted Convex-Concave Nonlinearity”, Math. Notes, 112:2 (2022), 251–270
Farman Mamedov, “On Harnack inequality and Hölder continuity to the degenerate parabolic equations”, Journal of Differential Equations, 340 (2022), 521
Farman Mamedov, Sara Monsurrò, “Sobolev inequality with non-uniformly degenerating gradient”, Electron. J. Qual. Theory Differ. Equ., 2022, no. 24, 1
Mamedov F., “A Poincare'S Inequality With Non-Uniformly Degenerating Gradient”, Mon.heft. Math., 194:1 (2021), 151–165
Mamedov F., Mammadzade N., Persson L.-E., “A New Fractional Order Poincare'S Inequality With Weights”, Math. Inequal. Appl., 23:2 (2020), 611–624
Mamedov F., Mammadli S., Shukurov Ya., “On Compact and Bounded Embedding in Variable Exponent Sobolev Spaces and Its Applications”, Arabian J. Math., 9:2 (2020), 401–414
Mamedov F., Shukurov Ya., “A Sawyer-Type Sufficient Condition For the Weighted Poincaré, Inequality”, Positivity, 22:3 (2018), 687–699
Maria Transirico, Sara Monsurrò, Farman Mamedov, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 793
Mamedov F.I., Ibragimov T.T., “On the behavior of solutions of some nonlinear degenerate elliptic inequalities”, Differ. Equ., 46:5 (2010), 711–721

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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