具有有限整数奇点的向量场在维度n中的弱和强L^p极限
Weak and strong $L^p$-limits of vector fields with finitely many integer singularities in dimension $n$
AI总结：
研究了具有有限整数奇点的向量场在不同维度下的L^p极限性质，证明了其在特定区域下的强L^p闭包和弱序列闭包特性。
摘要：
对于给定的p∈[1,+∞)和n∈N，n≥1，作者确定了具有有限整数拓扑奇点的向量场类在特定区域D的强L^p闭包L_{Z}^p(D)。此外，对于n≥2的每个n，当D是R^n中的开区域且与开单位立方体bi-Lipschitz等价时，L_{Z}^p(D)对于每个p∈(1,+∞)是弱序列闭的。先前分析的副产品是通过其奇点集的连接性得到了此类对象的有用刻画。
英文摘要：
For every given $p\in [1,+\infty)$ and $n\in\mathbb{N}$ with $n\ge 1$, the authors identify the strong $L^p$-closure $L_{\mathbb{Z}}^p(D)$ of the class of vector fields having finitely many integer topological singularities on a domain $D$ which is either bi-Lipschitz equivalent to the open unit $n$-dimensional cube or to the boundary of the unit $(n+1)$-dimensional cube. Moreover, for every $n\in\mathbb{N}$ with $n\ge 2$ the authors prove that $L_{\mathbb{Z}}^p(D)$ is weakly sequentially closed for every $p\in (1,+\infty)$ whenever $D$ is an open domain in $\mathbb{R}^n$ which is bi-Lipschitz equivalent to the open unit cube. As a byproduct of the previous analysis, a useful characterisation of such class of objects is obtained in terms of existence of a (minimal) connection for their singular set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
