The variable exponent Sobolev capacity and quasi-fine properties of Sobolev functions in the case p−=1

In this article we extend the known results concerning the subadditivity of capacity and the Lebesgue points of functions of the variable exponent Sobolev spaces to cover also the case p−=1. We show that the variable exponent Sobolev capacity is subadditive for variable exponents satisfying 1⩽p

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-04, Vol.412 (1), p.168-180
Main Authors: Hakkarainen, Heikki, Nuortio, Matti
Format: Article
Language:English
Subjects:
Capacity
Lebesgue points
Non-uniformly convex energy
Quasicontinuity
Sobolev capacity
Variable exponent
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Summary:In this article we extend the known results concerning the subadditivity of capacity and the Lebesgue points of functions of the variable exponent Sobolev spaces to cover also the case p−=1. We show that the variable exponent Sobolev capacity is subadditive for variable exponents satisfying 1⩽p
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.08.063