THE DIRICHLET PROBLEM FOR THE UNIFORMLY ELLIPTIC EQUATION IN GENERALIZED WEIGHTED MORREY SPACES

被引：2
|
作者：
Gadjiev, Tahir S. [1 ]
Culiyev, Vacif S. [1 ,2 ,3 ]
Suleymanova, Konul C. [1 ]
机构：
[1] Inst Math & Mech, Baku, Azerbaijan
[2] Baku State Univ, Inst Appl Math, Baku, Azerbaijan
[3] Dumlupinar Univ, Dept Math, Kutahya, Turkey
来源：
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2020年 / 57卷 / 01期
关键词：
Generalized weighted Morrey spaces; uniformly higher-order elliptic equations; a priori estimates; commutators; VMO; SINGULAR INTEGRAL-OPERATORS; PARABOLIC EQUATIONS; MAXIMAL OPERATOR; BOUNDARY; COMMUTATORS; INEQUALITIES; BOUNDEDNESS; REGULARITY;
D O I：
10.1556/012.2020.57.1.1449
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 arid 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 Omega subset of R-n are obtained.
引用
收藏
页码：68 / 90
页数：23
相关论文
共 50 条
  • [1] THE DIRICHLET PROBLEM IN A CLASS OF GENERALIZED WEIGHTED MORREY SPACES
    Guliyev, Vagif S.
    Omarova, Mehriban N.
    Softova, Lubomira
    [J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2019, 45 (02): : 270 - 285
  • [2] A remark on estimates for uniformly elliptic operators on weighted Lp spaces and Morrey spaces
    Kurata, K
    Sugano, S
    [J]. MATHEMATISCHE NACHRICHTEN, 2000, 209 : 137 - 150
  • [3] Dirichlet problem for elliptic equations with coefficients in locally Morrey spaces
    Di Gironimo, Patrizia
    [J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2020, 23 (06) : 1109 - 1120
  • [4] Dirichlet boundary value problems for uniformly elliptic equations in modified local generalized Sobolev-Morrey spaces
    Guliyev, Vagif S.
    Gadjiev, Tahir S.
    Galandarova, Shahla
    [J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2017, (71) : 1 - 17
  • [5] Weighted Morrey Regularity of Weak Solutions for Degenerate Elliptic Dirichlet Problem
    Cui, Xuewei
    Niu, Pengcheng
    [J]. PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON INFORMATION AND MANAGEMENT SCIENCES, 2010, 9 : 488 - 491
  • [6] The Regularity Problem for Uniformly Elliptic Operators in Weighted Spaces
    Li Chen
    José María Martell
    Cruz Prisuelos-Arribas
    [J]. Potential Analysis, 2023, 58 : 409 - 439
  • [7] The Regularity Problem for Uniformly Elliptic Operators in Weighted Spaces
    Chen, Li
    Maria Martell, Jose
    Prisuelos-Arribas, Cruz
    [J]. POTENTIAL ANALYSIS, 2023, 58 (03) : 409 - 439
  • [8] Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces
    Ouaarabi, Mohamed El
    Abbassi, Adil
    Allalou, Chakir
    [J]. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2021, 7 (01) : 221 - 242
  • [9] Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces
    Mohamed El Ouaarabi
    Adil Abbassi
    Chakir Allalou
    [J]. Journal of Elliptic and Parabolic Equations, 2021, 7 : 221 - 242
  • [10] Elliptic Systems in Generalized Morrey Spaces
    Palagachev, D. K.
    Softova, L. G.
    [J]. AZERBAIJAN JOURNAL OF MATHEMATICS, 2021, 11 (02): : 153 - 162
12345