Title | Fractional Sobolev regularity for the Brouwer degree |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | De Lellis C., Inauen D. |

Journal | Communications in Partial Differential Equations |

Volume | 42 |

Pagination | 1510–1523 |

Date Published | October |

Publisher | Taylor & Francis |

Type of Article | other |

ISSN | 0360-5302 |

Abstract | We prove that if ??$R$n is a bounded open set and n\ensuremathα\ensuremath>dimb(??) = d, then the Brouwer degree deg(v,?,$\cdot$) of any Hölder function belongs to the Sobolev space for every . This extends a summability result of Olbermann and in fact we get, as a byproduct, a more elementary proof of it. Moreover, we show the optimality of the range of exponents in the following sense: for every \ensuremathβ?0 and p?1 with there is a vector field with deg (v,?,$\cdot$)?W\ensuremathβ,p, where is the unit ball. |

Notes | Comm. Partial Differential Equations 42 (2017), no. 10, 1510–1523. |

URL | https://www.tandfonline.com/doi/abs/10.1080/03605302.2017.1380040 |

DOI | 10.1080/03605302.2017.1380040 |

Order:

4