Characterization of Sobolev and BV spaces

Giovanni Leoni*, Eli Spector

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The main results of this paper are new characterizations of W1,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 languageEnglish
Pages (from-to)2926-2958
Number of pages33
JournalJournal of Functional Analysis
Issue number10
StatePublished - 15 Nov 2011


  • Functions of bounded variation
  • Non-local functionals
  • Sobolev spaces

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