The Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2023-07-19 DOI:10.57262/ade029-0506-389

Y. Giga, Zhongyang Gu

引用次数: 0

Abstract

We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n \geq 3$, we establish its Helmholtz decomposition for arbitrary uniformly $C^3$ domain in $\mathbf{R}^n$.

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一般无界域中 $BMO$ 类型向量场的赫尔姆霍兹分解

我们考虑了一个具有有界均值振荡的 $L^2$ 向量场空间，它的边界 "法向 "分量是很好控制的。在维数为 $n\geq 3$ 的情况下，我们为 $\mathbf{R}^n$ 中任意均匀的 $C^3$ 域建立了它的亥姆霍兹分解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.