### 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) |
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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 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Advances in Differential Equations*,

*23*(3-4), 295-328.

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*Advances in Differential Equations*, vol. 23, no. 3-4, pp. 295-328.

**The Friedrichs extension for elliptic wedge operators of second order.** / Krainer, Thomas; Mendoza, Gerardo A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Friedrichs extension for elliptic wedge operators of second order

AU - Krainer, Thomas

AU - Mendoza, Gerardo A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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 = IF ⊕ IaF and there is a natural map P: C∞(Y;IF) → C∞(M; E) such that CIF ∞(M; E) = P(C∞(Y;IF)) + Ċ∞(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF ∞(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.

AB - 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 = IF ⊕ IaF and there is a natural map P: C∞(Y;IF) → C∞(M; E) such that CIF ∞(M; E) = P(C∞(Y;IF)) + Ċ∞(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF ∞(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.

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M3 - Article

VL - 23

SP - 295

EP - 328

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 3-4

ER -