The Calderón projection: New definition and applications

By Bernhelm Booss-Bavnbek, M. Lesch, Chaofeng Zhu. 2008

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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 Σ . We describe the analytic and topological properties of A in a collar neighborhood U of Σ 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 self-adjoint Fredholm extensions under continuous variation of the data.

Subfields: Applied Mathematics, Mathematical Physics

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