Characterization of Sobolev and BV spaces

Giovanni Leoni; Eli Spector

doi:10.1016/j.jfa.2011.07.018

Characterization of Sobolev and BV spaces

Giovanni Leoni^*, Eli Spector

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

The main results of this paper are new characterizations of W^1,p(<), 1<p<∞, and BV(Ω) for Ω⊂R{double-struck}^N an arbitrary open set. Using these results, we answer some open questions of Brezis (2002) [10] and Ponce (2004) [25].

Original language	English
Pages (from-to)	2926-2958
Number of pages	33
Journal	Journal of Functional Analysis
Volume	261
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2011.07.018
State	Published - 15 Nov 2011

Keywords

Functions of bounded variation
Non-local functionals
Sobolev spaces

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title = "Characterization of Sobolev and BV spaces",

abstract = "The main results of this paper are new characterizations of W1,p(<), 1N an arbitrary open set. Using these results, we answer some open questions of Brezis (2002) [10] and Ponce (2004) [25].",

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KW - Functions of bounded variation

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Characterization of Sobolev and BV spaces

Abstract

Keywords

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