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Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2005 (English)In: Journal of Functional Analysis, ISSN 0022-1236, Vol. 224, no 2, 408-430 p.Article in journal (Refereed) Published
Abstract [en]

In 1972 the author proved the so-called conductor and capacitary inequalities for the Dirichlet-type integrals of a function on a Euclidean domain. Both were used to derive necessary and sufficient conditions for Sobolev-type inequalities involving arbitrary domains and measures. The present article contains new conductor inequalities for nonnegative functionals acting on functions defined on topological spaces. Sharp capacitary inequalities, stronger than the classical Sobolev inequality, with the best constant and the sharp from of the Yudovich inequality (Soviet Math. Dokl. 2 (1961) 746) due to Moser (Indiana Math. J. (1971) 1077) are found. © 2004 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2005. Vol. 224, no 2, 408-430 p.
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URN: urn:nbn:se:liu:diva-35977DOI: 10.1016/j.jfa.2004.09.009Local ID: 29246OAI: diva2:256825
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-12

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Maz´ya, Vladimir G.
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