### Abstract

Let Ω be a domain in ℝ^{n}, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms f_{k} : Ω → ℝ^{n} with positive Jacobian determinants, J(x, f_{k}) > 0, converges weakly in W^{1,p}(Ω, ℝ^{n}), for some p ≥ 1, to a mapping f. We show that J(x, f) ≥ 0 a.e. in Ω. Generalizations to higher dimensions are also given.

Original language | English (US) |
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Pages (from-to) | 65-73 |

Number of pages | 9 |

Journal | Advances in Calculus of Variations |

Volume | 11 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

### Keywords

- Jacobian
- Sobolev homeomorphism
- weak limits

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Hencl, S., & Onninen, J. (2018). Jacobian of weak limits of Sobolev homeomorphisms.

*Advances in Calculus of Variations*,*11*(1), 65-73. https://doi.org/10.1515/acv-2016-0005