## Abstract

This paper concerns Hodge-Dirac operators D_{H} = d + δ acting in L^{p}(Ω,Λ) where Ω is a bounded open subset of ℝ^{n} satisfying some kind of Lipschitz condition, Λ is the exterior algebra of ℝ^{n}, d is the exterior derivative acting on the de Rham complex of differential forms on Ω, and δ is the interior derivative with tangential boundary conditions. In L^{2}(Ω,Λ), d' = δ and D_{H} is self-adjoint, thus having bounded resolvent {(I + itD_{H})}^{{t}^{∈R}} as well as a bounded functional calculus in L2(Ω,Λ). We investigate the range of values pH < p < p^{H} about p = 2 for which D_{H} has bounded resolvents and a bounded holomorphic functional calculus in L p(Ω,Λ).

Original language | English |
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Title of host publication | Mathematical Analysis, Probability and Applications – Plenary Lectures - ISAAC 2015 |

Editors | Tao Qian, Luigi G. Rodino |

Publisher | Springer New York LLC |

Pages | 55-75 |

Number of pages | 21 |

ISBN (Print) | 9783319419435 |

DOIs | |

Publication status | Published - 2016 |

Event | 10th International Society of Analysis, its Applications and Computation, ISAAC 2015 - Macau, China Duration: 3 Aug 2015 → 8 Aug 2015 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 177 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | 10th International Society of Analysis, its Applications and Computation, ISAAC 2015 |
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Country/Territory | China |

City | Macau |

Period | 3/08/15 → 8/08/15 |

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