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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Hakkarainen, Heikki¹  Nuortio, Matti¹ 

[1] Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland

关键词: Capacity;    Sobolev capacity;    Variable exponent;    Non-uniformly convex energy;    Lebesgue points;    Quasicontinuity;   

DOI  :  10.1016/j.jmaa.2013.08.063

来源: Elsevier

【 摘 要 】

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 < infinity. Furthermore, we show that if the exponent is log-Holder continuous, then the functions of the variable exponent Sobolev spaces have Lebesgue points quasieverywhere and they have quasicontinuous representatives also in the case p(-) = 1. To gain these results we develop methods that are not reliant on reflexivity or maximal function arguments. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free