论文标题
分数Sobolev空间具有部分消失的痕量条件的扩展问题
The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
论文作者
论文摘要
We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of $O$.集合$ o $应该满足所谓的内部厚度条件，$ \ partial o \ setminus d $，它比全球内部厚度条件弱得多。该证明是通过减少案例$ d = \ emptyset $使用几何结构来起作用的。
We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of $O$. The set $O$ is supposed to satisfy the so-called interior thickness condition in $\partial O \setminus D$, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case $D=\emptyset$ using a geometric construction.
