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Hardy's Inequality for W0 1,p-Functions on Riemannian Manifolds

Vladimir M. Miklyukov and Matti K. Vuorinen
Proceedings of the American Mathematical Society
Vol. 127, No. 9 (Sep., 1999), pp. 2745-2754
Stable URL: http://www.jstor.org/stable/119576
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hardy's Inequality for W0
1,p-Functions on Riemannian Manifolds
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Abstract

We prove that for every Riemannian manifold χ with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class W0 1,p(χ ). 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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