Characterization of Sobolev and BV spaces

Giovanni Leoni; Daniel Spector

doi:10.1016/j.jfa.2011.07.018

Characterization of Sobolev and BV spaces

Giovanni Leoni^*, Daniel Spector

^*Corresponding author for this work

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

52 Citations (Scopus)

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
Publication status	Published - 2011 Nov 15
Externally published	Yes

Keywords

Functions of bounded variation
Non-local functionals
Sobolev spaces

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2011.07.018

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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].",

keywords = "Functions of bounded variation, Non-local functionals, Sobolev spaces",

author = "Giovanni Leoni and Daniel Spector",

note = "Funding Information: The authors warmly thank the Center for Nonlinear Analysis (NSF Grant Nos. DMS-0405343 and DMS-0635983), where this research was carried out. The research of G. Leoni and D. Spector was partially funded by the National Science Foundation under Grant Nos. DMS-0708039 and DMS-1007989.",

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AU - Leoni, Giovanni

AU - Spector, Daniel

N1 - Funding Information: The authors warmly thank the Center for Nonlinear Analysis (NSF Grant Nos. DMS-0405343 and DMS-0635983), where this research was carried out. The research of G. Leoni and D. Spector was partially funded by the National Science Foundation under Grant Nos. DMS-0708039 and DMS-1007989.

PY - 2011/11/15

Y1 - 2011/11/15

N2 - 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].

AB - 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].

KW - Functions of bounded variation

KW - Non-local functionals

KW - Sobolev spaces

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JF - Journal of Functional Analysis

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ER -

Characterization of Sobolev and BV spaces

Abstract

Keywords

ASJC Scopus subject areas

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