The Calderon projection: New definition and applications

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Booss-Bavnbek, Bernhelm²  Lesch, Matthias¹  Zhu, Chaofeng³ 

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

[2] Roskilde Univ, Dept Sci Syst & Models, DK-4000 Roskilde, Denmark

[3] Nankai Univ, Chem Inst Math, Tianjin 300071, Peoples R China

关键词: Calderon projection;    Cauchy data spaces;    Cobordism theorem;    Continuous variation of operators and boundary conditions;    Elliptic differential operator;    Ellipticity with parameter;    Lagrangian subspaces;    Regular boundary value problem;    Sectorial projection;    Self-adjoint Fredholm extension;    Sobolev spaces;    Symplectic functional analysis;   

DOI  :  10.1016/j.geomphys.2009.03.012

来源: Elsevier

【 摘 要 】

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 Sigma. We describe the analytic and topological properties of A in a collar neighborhood U of Sigma and analyze various ways of writing A(sic) 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. (C) 2009 Elsevier B.V. All rights reserved.

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