## Abstract

Let be an open set in R_{n} and suppose that is a Sobolev homeomorphism. We study the regularity of f _{-1} under the L _{p}-integrability assumption on the distortion function K f. First, if is the unit ball and p > n-1, then the optimal local modulus of continuity of f _{-1} is attained by a radially symmetric mapping. We show that this is not the case when p n-1 and n ≥3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for Df _{-1} in terms of the L _{p}-integrability assumptions of K f.

Original language | English (US) |
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Pages (from-to) | 647-663 |

Number of pages | 17 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 146 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2016 |

Externally published | Yes |

## Keywords

- Sobolev homeomorphism
- higher integrability
- mappings of finite distortion
- modulus of continuity
- regularity of the inverse

## ASJC Scopus subject areas

- Mathematics(all)

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