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March/April 2018 The Friedrichs extension for elliptic wedge operators of second order
Gerardo A. Mendoza, Thomas Krainer
Adv. Differential Equations 23(3/4): 295-328 (March/April 2018).

Abstract

Let ${\mathcal M}$ be a smooth compact manifold whose boundary is the total space of a fibration ${\mathcal N}\to {\mathcal Y}$ with compact fibers, let $E\to{\mathcal M}$ be a vector bundle. Let \begin{equation} A:C_c^\infty( \overset{\,\,\circ} {\mathcal M};E)\subset x^{-\nu} L^2_b({\mathcal M};E)\to x^{-\nu} L^2_b({\mathcal M};E) $ \tag*{(†)} \end{equation} 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 $\nu$ splits as a direct sum ${\mathscr T}={\mathscr T}_F\oplus{\mathscr T}_{aF}$ and there is a natural map ${\mathfrak P} :C^\infty({\mathcal Y};{\mathscr T}_F)\to C^\infty( \overset{\,\,\circ} {\mathcal M};E)$ such that $C^\infty_{{\mathscr T}_F}({\mathcal M};E)={\mathfrak P} (C^\infty({\mathcal Y};{\mathscr T}_F)) +\dot C^\infty({\mathcal M};E)\subset {\mathcal D}_{\max}(A)$. It is shown that the closure of $A$ when given the domain $C^\infty_{{\mathscr T}_F}({\mathcal M};E)$ 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.

Citation

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Gerardo A. Mendoza. Thomas Krainer. "The Friedrichs extension for elliptic wedge operators of second order." Adv. Differential Equations 23 (3/4) 295 - 328, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 1380.58021
MathSciNet: MR3738648

Subjects:
Primary: 35J47, 35J57, 58J05, 58J32

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 3/4 • March/April 2018
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