$B^3$上具有2个整数奇点的向量场的强$L^p$ -闭包
The strong $L^p$-closure of vector fields with finitely many integer singularities on $B^3$
摘要：
本文研究了开单位球$B\subset\mathbb{R}^3$上光滑到n个整数点奇点的向量场的强$L^p$ -闭包$L_{\mathbb{Z}}^p(B)$.首先，这种强封闭的特点是任意$p\in[1,+\infty)$。其次，它表明会发生什么，如果可积阶$p$是足够大（即，如果$p\ge 3/2$）。最后，给出了$L_{\mathbb{Z}}^1(B)$中元素的分解定理，给出了在有限质量的$B$上通过质量最小化的整数1-流连接这种向量场的奇异集的可能性。
英文摘要：
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.
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。
