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    Elliptic systems of variable order

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    Genre
    Journal Article
    Date
    2015-01-01
    Author
    Krainer, T
    Mendoza, GA
    Subject
    Manifolds with edge singularities
    elliptic operators
    boundary value problems
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5839
    
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    DOI
    10.4171/rmi/829
    Abstract
    © European Mathematical Society. The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general smooth fiberwise multiplicative group actions. These actions, essentially trivial (and therefore invisible) in the case of regular boundary value problems, are intimately connected with what passes for Poisson and trace operators, and to pseudodifferential boundary conditions in the more general situation. Here the part of the theory pertaining to pseudodifferential operators is presented in its entirety. The symbols for these are defined with the aid of an intertwining of the actions. Also presented here are the ancillary Sobolev spaces, an index theorem for the elliptic elements of the pseudodifferential calculus, and essential ingredients for analyzing boundary conditions of Atiyah-Patodi-Singer type in the more general theory.
    Citation to related work
    European Mathematical Society Publishing House
    Has part
    Revista Matematica Iberoamericana
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5821
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