A geometrical version of Hardy’s inequality for \stackrel{∘}𝑊^{1,𝑝}(Ω)

Tidblom, Jesper

doi:10.1090/S0002-9939-04-07526-4

A geometrical version of Hardy’s inequality for $\stackrel {\circ }{\textrm {W}}{}^{1,p}(\Omega )$
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Proc. Amer. Math. Soc. 132 (2004), 2265-2271 Request permission

Abstract:

The aim of this article is to prove a Hardy-type inequality, concerning functions in $\stackrel {\circ }{\textrm {W}}{\!}^{1,p}(\Omega )$ for some domain $\Omega \subset R^n$, involving the volume of $\Omega$ and the distance to the boundary of $\Omega$. The inequality is a generalization of a recently proved inequality by M. Hoffmann–Ostenhof, T. Hoffmann–Ostenhof and A. Laptev (2002), which dealt with the special case $p=2$.

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