### 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) |
---|---|

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 |

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### Keywords

- Jacobian
- Sobolev homeomorphism
- weak limits

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Advances in Calculus of Variations*,

*11*(1), 65-73. https://doi.org/10.1515/acv-2016-0005

**Jacobian of weak limits of Sobolev homeomorphisms.** / Hencl, Stanislav; Onninen, Jani Kristian.

Research output: Contribution to journal › Article

*Advances in Calculus of Variations*, vol. 11, no. 1, pp. 65-73. https://doi.org/10.1515/acv-2016-0005

}

TY - JOUR

T1 - Jacobian of weak limits of Sobolev homeomorphisms

AU - Hencl, Stanislav

AU - Onninen, Jani Kristian

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let Ω be a domain in ℝn, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms fk : Ω → ℝn with positive Jacobian determinants, J(x, fk) > 0, converges weakly in W1,p(Ω, ℝn), 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.

AB - Let Ω be a domain in ℝn, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms fk : Ω → ℝn with positive Jacobian determinants, J(x, fk) > 0, converges weakly in W1,p(Ω, ℝn), 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.

KW - Jacobian

KW - Sobolev homeomorphism

KW - weak limits

UR - http://www.scopus.com/inward/record.url?scp=85040164809&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040164809&partnerID=8YFLogxK

U2 - 10.1515/acv-2016-0005

DO - 10.1515/acv-2016-0005

M3 - Article

AN - SCOPUS:85040164809

VL - 11

SP - 65

EP - 73

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

SN - 1864-8258

IS - 1

ER -