Another approach to biting convergence of Jacobians

Luigi Greco, Tadeusz Iwaniec, Uma Subramanian

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We give new proof of the theorem of K. Zhang [Z] on biting convergence of Jacobian determinants for mappings of Sobolev class script W sign 1,n(Ω, ℝn). The novelty of our approach is in using script W sign1,p-estimates with the exponents 1 ≤ p < n, as developed in [IS1], [IL], [I1]. These rather strong estimates compensate for the lack of equi-integrability. The remaining arguments are fairly elementary. In particular, we are able to dispense with both the Chacon biting lemma and the Dunford-Pettis criterion for weak convergence in ℒ 1(Ω). We extend the result to the so-called Grand Sobolev setting. Biting convergence of Jacobians for mappings whose cofactor matrices are bounded in ℒn/n-1 (ℝn) is also obtained. Possible generalizations to the wedge products of differential forms are discussed.

Original languageEnglish (US)
Pages (from-to)815-830
Number of pages16
JournalIllinois Journal of Mathematics
Issue number3
StatePublished - 2003

ASJC Scopus subject areas

  • General Mathematics


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