Poincaré inequality on subanalytic sets

英文摘要：

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 $u_Ω:=\frac{1}{|Ω|}\int_Ω u.$