论文标题
庞加莱对亚分析集的不平等
Poincaré inequality on subanalytic sets
论文作者
论文摘要
令$ω$为$ \ mathbb {r}^n $的子分析有限的开放子集，可能是单数边界。我们表明，给定的$ p \在[1，\ infty）$中，有一个常数$ c $，因此对于任何$ u \ in W^{1，p}（ω）$中的任何$ u \我们有$ || u-u-u-u_Ω|| u-u-u _ {l^p} l^p} $u_Ω：= \ frac {1} {|ω|} \int_Ωu。$
Let $Ω$ be a subanalytic bounded open subset of $\mathbb{R}^n$, with possibly singular boundary. We show that given $p\in [1,\infty)$, there is a constant $C$ such that for any $u\in W^{1,p}(Ω)$ we have $||u-u_Ω||_{L^p} \le C||\nabla u||_{L^p},$ where we have set $u_Ω:=\frac{1}{|Ω|}\int_Ω u.$
