论文标题
强的$ l^p $ - 在$ b^3 $上有限许多整数奇点的矢量场
The strong $L^p$-closure of vector fields with finitely many integer singularities on $B^3$
论文作者
论文摘要
本文的目的是研究强$ l^p $ cluber $ l _ {\ mathbb {z}}^p（b）p（b）$ ball $ b \ subset \ subset \ subset \ mathbb {r}^3 $，它们非常顺畅，以有限地获得许多integer Point Singularities。首先，在[1，+\ infty）$中的任意$ p \ $ p \的特征是如此强大的关闭。其次，显示如果可集成订单$ p $足够大（即，如果$ p \ ge 3/2 $）会发生什么。最终，给出了$ l _ {\ mathbb {z}}^1（b）$中元素的分解定理，以通过$ b $与有限质量连接$ b $的$ by by by b $ b $ by in Integer 1-Current通过质量限制，Integer 1-Current连接此类矢量字段的可能性。
This paper is aimed to investigate the strong $L^p$-closure $L_{\mathbb{Z}}^p(B)$ of the vector fields on the open unit ball $B\subset\mathbb{R}^3$ that are smooth up to finitely many integer point singularities. First, such strong closure is characterized for arbitrary $p\in[1,+\infty)$. Secondly, it is shown what happens if the integrability order $p$ is large enough (namely, if $p\ge 3/2$). Eventually, a decomposition theorem for elements in $L_{\mathbb{Z}}^1(B)$ is given, conveying information about the possibility of connecting the singular set of such vector fields by a mass-minimizing, integer 1-current on $B$ with finite mass.
