$W^{1,p}(B^3;S^2)$中光滑映射的闭包
Closure of Smooth Maps in $W^{1,p}(B^3;S^2)$
摘要：
对于每一个$2 < p < 3$，我们表明，$u \in W^{1,p}(B^3; S^2)$可以强近似的映射在$C^\infty(\Bar{B}^3; S^2)$当且仅当，分布雅可比矩阵的$u$消失相同。这个结果最初是由Bethuel-Coron-Demengel-Helein证明的，但是我们提出了一个不同的策略，它是由$W^{2,p}$ -情况所激发的。
英文摘要：
For every $2 < p < 3$, we show that $u \in W^{1,p}(B^3; S^2)$ can be strongly approximated by maps in $C^\infty(\Bar{B}^3; S^2)$ if, and only if, the distributional Jacobian of $u$ vanishes identically. This result was originally proved by Bethuel-Coron-Demengel-Helein, but we present a different strategy which is motivated by the $W^{2,p}$-case.
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。
