H1-estimates of Jacobians by subdeterminants

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Abstract

Let f : Ω → ℝn be a mapping in the Sobolev space, Wloc1,n-1 (Ω, ℝn), n ≥ 2. We assume that the cofactors of the differential matrix Df (x) belong to Ln/n-1 (Ω). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space H1 (Ω).

Original languageEnglish (US)
Pages (from-to)341-358
Number of pages18
JournalMathematische Annalen
Volume324
Issue number2
DOIs
StatePublished - Dec 1 2002

ASJC Scopus subject areas

  • Mathematics(all)

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