广义加权Morrey空间中一致椭圆方程的Dirichlet问题

IF 0.4 4区 数学 Q4 MATHEMATICS
T. Gadjiev, V. Guliyev, Konul G. Suleymanova
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引用次数: 4

摘要

本文通过建立调和分析中Hardy-Littlewood算子和Calderon-Zygmund奇异积分算子在广义加权Morrey空间中的有界性,从Muckenhoupt类Ap中得到了带权的广义加权Sobolev-Morrey估计。由此,得到了光滑有界Ω∧∈n上广义加权Sobolev-Morrey空间中高阶Dirichlet边界问题一致椭圆方程弱解的先验估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces
In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap 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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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
19
审稿时长
>12 weeks
期刊介绍: The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.
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