论文标题
弱和强的$ l^p $ - 矢量场的限制有限的整数奇点$ n $
Weak and strong $L^p$-limits of vector fields with finitely many integer singularities in dimension $n$
论文作者
论文摘要
对于[1，+\ infty）$和$ n \ in \ mathbb {n} $带有$ n \ ge 1 $的每个给定的$ p \，作者确定了强的$ l^p $ -l^p $ l _ {\ mathbb {z}}}^p（z}}}^p（d）$ nip inip in toblodice toblodice toblodice toblodice toblodice toblodice toblodice toblodice toblodice toblodice toblodies相当于开放单元$ n $维立方体或单元$（n+1）$ - 尺寸立方体的边界。 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相当于开放单元立方体。作为先前分析的副产品，根据其单数集的（最小）连接的存在，可以获得此类对象类别的有用表征。
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.
