### Abstract

Let F: Ω → ℝ
^{n} be a mapping in the Sobolev space W
^{1,n-1}(Ω,ℝ
^{n}), n > 2. We assume that the determinant of the differential matrix DF (x) is nonnegative, while the cofactor matrix D
^{#}F satisfies |D
^{#}f|n/n 1 ε L
^{P}(ω), where L
^{p}(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in L
_{loc}
^{1} (Ω). Estimates above and below L
_{loc}
^{1} (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix.

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

Pages (from-to) | 223-254 |

Number of pages | 32 |

Journal | Journal of Geometric Analysis |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 2002 |

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### Keywords

- cofactor matrix
- distributional Jacobian
- integrability of Jacobian
- Orlicz space

### ASJC Scopus subject areas

- Mathematics(all)
- Geometry and Topology

### Cite this

*Journal of Geometric Analysis*,

*12*(2), 223-254. https://doi.org/10.1007/BF02922041