Hardy’s inequality for 𝑊^{1,𝑝}₀-functions on Riemannian manifolds

Miklyukov, Vladimir; Vuorinen, Matti

doi:10.1090/S0002-9939-99-04849-2

Hardy’s inequality for $W^{1,p}_0$-functions on Riemannian manifolds
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by Vladimir M. Miklyukov and Matti K. Vuorinen

Proc. Amer. Math. Soc. 127 (1999), 2745-2754

DOI: https://doi.org/10.1090/S0002-9939-99-04849-2

Published electronically: April 23, 1999

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Abstract:

We prove that for every Riemannian manifold $\mathcal {X}$ with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class $W_0^{1,p}( \mathcal {X})$. We also study manifolds satisfying Hardy’s inequality and, in particular, we establish an estimate for the rate of growth of the weighted volume of the noncompact part of such a manifold.

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