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.
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收藏
页码：68 / 90
页数：23
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