论文标题
从Sobolev到$ BV $的扩展域的零音量边界
Zero volume boundary for extension domains from Sobolev to $BV$
论文作者
论文摘要
在本说明中，我们证明了$（w^{1，p}，bv）$ - 扩展域的边界在域$ \ boz $是$ 1 $ -FAT的假设下，几乎每个$ x \ in \ in \ in \ partial \ boz $。尤其是，任何平面$（W^{1，P}，BV）$的边界 - 扩展域是零量的。
In this note, we prove that the boundary of a $(W^{1, p}, BV)$-extension domain is of volume zero under the assumption that the domain $\boz$ is $1$-fat at almost every $x\in\partial\boz$. Especially, the boundary of any planar $(W^{1, p}, BV)$-extension domain is of volume zero.
