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Conductor inequalities and criteria for Sobolev type two-weight imbeddings
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2006 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 194, no 1 SPEC. ISS., 94-114 p.Article in journal (Refereed) Published
Abstract [en]

A typical inequality handled in this article connects the Lp-norm of the gradient of a function to a one-dimensional integral of the p-capacitance of the conductor between two level surfaces of the same function. Such conductor inequalities lead to necessary and sufficient conditions for multi-dimensional and one-dimensional Sobolev type inequalities involving two arbitrary measures. Compactness criteria and two-sided estimates for the essential norm of the related imbedding operator are obtained. Some counterexamples are presented to illustrate the peculiarities arising in the case of higher derivatives. Criteria for two-weight inequalities with fractional Sobolev norms of order l < 2 are found.

Place, publisher, year, edition, pages
2006. Vol. 194, no 1 SPEC. ISS., 94-114 p.
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URN: urn:nbn:se:liu:diva-35990DOI: 10.1016/ ID: 29264OAI: diva2:256838
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2010-06-09

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Maz´ya, Vladimir G.
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The Institute of TechnologyApplied Mathematics
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