## Abstract

Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = I_{F} ⊕ I_{aF} and there is a natural map P: C^{∞}(Y;I_{F}) → C^{∞}(M; E) such that C_{IF}^{∞}(M; E) = P(C^{∞}(Y;I_{F})) + Ċ^{∞}(M;E) ⊂ D_{max}(A). It is shown that the closure of A when given the domain C_{IF}^{∞}(M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.

Original language | English (US) |
---|---|

Pages (from-to) | 295-328 |

Number of pages | 34 |

Journal | Advances in Differential Equations |

Volume | 23 |

Issue number | 3-4 |

State | Published - Mar 1 2018 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics