### Abstract

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, ℝ^{n}). The novelty of our approach is in using script W sign^{1,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 ℒ^{n/n-1} (ℝ^{n}) is also obtained. Possible generalizations to the wedge products of differential forms are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 815-830 |

Number of pages | 16 |

Journal | Illinois Journal of Mathematics |

Volume | 47 |

Issue number | 3 |

State | Published - Sep 1 2003 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Another approach to biting convergence of Jacobians'. Together they form a unique fingerprint.

## Cite this

*Illinois Journal of Mathematics*,

*47*(3), 815-830.