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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hardy's inequality for $W_0^{1,p}$-functions
on Riemannian manifolds


Authors: Vladimir M. Miklyukov and Matti K. Vuorinen
Journal: Proc. Amer. Math. Soc. 127 (1999), 2745-2754
MSC (1991): Primary 53C21
Published electronically: April 23, 1999
MathSciNet review: 1600117
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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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Additional Information

Vladimir M. Miklyukov
Affiliation: Department of Mathematics, Volgograd State University, 2 Prodolnaya 30, Volgograd 400062, Russia
Address at time of publication: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: miklukov@math.vgu.tsaritsyn.su, miklyuk@math.byu.edu

Matti K. Vuorinen
Affiliation: Department of Mathematics, P.O.Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland
Email: vuorinen@csc.fi

DOI: https://doi.org/10.1090/S0002-9939-99-04849-2
Received by editor(s): May 20, 1997
Received by editor(s) in revised form: November 24, 1997
Published electronically: April 23, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society