The variable exponent BV-Sobolev capacity

In this article we study basic properties of the mixed BV-Sobolev capacity with variable exponent . We give an alternative way to define the mixed type BV-Sobolev-space which was originally introduced by Harjulehto, Hästö, and Latvala. Our definition is based on relaxing the -energy functional with...

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Bibliographic Details
Published in:Revista matemática complutense 2014, Vol.27 (1), p.13-40
Main Authors: Hakkarainen, Heikki, Nuortio, Matti
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Topology
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Summary:In this article we study basic properties of the mixed BV-Sobolev capacity with variable exponent . We give an alternative way to define the mixed type BV-Sobolev-space which was originally introduced by Harjulehto, Hästö, and Latvala. Our definition is based on relaxing the -energy functional with respect to the Lebesgue space topology. We prove that this procedure produces a Banach space that coincides with the space defined by Harjulehto et al. for a bounded domain and a log-Hölder continuous exponent . Then we show that this induces a type of variable exponent BV-capacity and that this is a Choquet capacity with many usual properties. Finally we prove that if is log-Hölder continuous, then this capacity has the same null sets as the variable exponent Sobolev capacity.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-012-0109-8