Estimates for capacities and traces of potentials

V. G. Maz'ja and S. P. Preobrazenskii

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-23

Abstract:

It is shown that isoperimetric inequalities, relating measures and capacities, hold for all sets in ℝ n if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel potential spaces are obtained. The introduction contains a survey of known results on inequalities of Sobolev type.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:297432

DOI: 10.1155/S0161171284000053

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