Abstract: We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic and topological properties of A in a collar neighborhood U of N and analyze various ways of writing A|U in product form. We discuss the sectorial projections of the corresponding tangential operator, construct various invertible doubles of A by suitable local boundary conditions, obtain Poisson type operators with different mapping properties, and provide a canonical construction of the Calderon projection. We apply our construction to generalize the Cobordism Theorem and to determine sufficient conditions for continuous variation of the Calderon projection and of well--posed selfadjoint Fredholm extensions under continuous variation of the data.
| Comments: | 60 pages, 4 figures; revised version; index and list of notation added; accepted for publication in J. Geom. Phys; v3 contains a few minor corrections |
| Subjects: | Differential Geometry (math.DG) ; Functional Analysis (math.FA) |
| MSC classes: | 58J32 (Primary); 35J67, 58J50, 57Q20 (Secondary) |
| Cite as: | arXiv:0803.4160 [math.DG] |
| (or arXiv:0803.4160v3 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.0803.4160 |
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DOI(s) linking to related resourcesFrom: Matthias Lesch [view email]
[v1] Fri, 28 Mar 2008 18:39:35 UTC (120 KB)
[v2] Sat, 4 Apr 2009 09:26:22 UTC (122 KB)
[v3] Mon, 27 Apr 2009 11:17:16 UTC (122 KB)
View a PDF of the paper titled The Calderon Projection: New Definition and Applications, by Bernhelm Booss-Bavnbek and 2 other authors