论文标题
关于BV功能的弱*和点收敛的注释
A note on the weak* and pointwise convergence of BV functions
论文作者
论文摘要
我们研究了弱*收敛序列的点融合属性$ \ {u_i \} _ {i \ in {\ mathbb n}} $ in $ \ mathrm {bv}（{\ Mathbb r}^n）$。我们表明，在通往合适的子序列（未重新标记）之后，我们在{\ Mathbb r}^n \ in {\ mathbb r}^n \ setMinus e $ in {\ mathbb r}^n \ setMinus e $ in {大多数$ n-1 $，另一方面，就$ | d u | $的cantor部分而言，也可以忽略不计。此外，我们讨论了这些结果的最佳性。
We study pointwise convergence properties of weakly* converging sequences $\{u_i\}_{i \in {\mathbb N}}$ in $\mathrm{BV}({\mathbb R}^n)$. We show that, after passage to a suitable subsequence (not relabeled), we have pointwise convergence $u_i^*(x)\to u^*(x)$ of the precise representatives for all $x\in {\mathbb R}^n \setminus E$, where the exceptional set $E \subset {\mathbb R}^n$ has on the one hand Hausdorff dimension at most $n-1$, and is on the other hand also negligible with respect to the Cantor part of $|D u|$. Furthermore, we discuss the optimality of these results.
