Poincar\'e inequality on subanalytic sets
Let $\Omega$ 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 $u\in W^{1,p}(\Omega)$ we have $||u-u_{\Omega}||_{L^p} \le C||\nabla u||_{L^p},$ where we have set $u_{\Omega}:=\frac{...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | Let $\Omega$ 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 $u\in W^{1,p}(\Omega)$ we have
$||u-u_{\Omega}||_{L^p} \le C||\nabla u||_{L^p},$ where we have set
$u_{\Omega}:=\frac{1}{|\Omega|}\int_{\Omega} u.$ |
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| DOI: | 10.48550/arxiv.2010.11529 |