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 = 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.
| 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 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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The Friedrichs extension for elliptic wedge operators of second order. / Krainer, Thomas; Mendoza, Gerardo A.
In: Advances in Differential Equations, Vol. 23, No. 3-4, 01.03.2018, p. 295-328.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
AN - SCOPUS:85038361267
VL - 23
SP - 295
EP - 328
JO - Advances in Differential Equations
JF - Advances in Differential Equations
SN - 1079-9389
IS - 3-4
ER -