The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

Tahir S. Gadjiev; Vagif S. Guliyev; Konul G. Suleymanova

doi:10.1556/012.2020.57.1.1449

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

Authors:

Tahir S. Gadjiev

Tahir S. Gadjiev Institute of Mathematics and Mechanics, Baku, Azerbaijan

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tgadjiev@mail.az

Vagif S. Guliyev

Vagif S. Guliyev Institute of Mathematics and Mechanics, Baku, Azerbaijan
Institute of Applied Mathematics, Baku State University, Baku, AzerbaijanDepartment of Mathematics, Dumlupinar University, Kutahya, Turkey

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vagif@guliyev.com

, and

Konul G. Suleymanova

Konul G. Suleymanova Institute of Mathematics and Mechanics, Baku, Azerbaijan

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ksuleymanova@mail.ru

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Pages:: 68–90

Online Publication Date:: Mar 2020

Publication Date:: 01 Mar 2020

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2020.57.1.1449

Keywords:: Primary 35J25; 42B20; 42B25; 42B35; Generalized weighted Morrey spaces; uniformly higher-order elliptic equations; a priori estimates; commutators

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Abstract

In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class A_p by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝⁿ are obtained.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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