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Realizations of Differential Operators on Conic Manifolds with Boundary

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Abstract

We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L p -Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    S. Coriasco

  2. Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    E. Schrohe

  3. Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    J. Seiler

Authors
  1. S. Coriasco
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  2. E. Schrohe
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  3. J. Seiler
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Correspondence to S. Coriasco.

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Mathematics Subject Classifications (2000): Primary 58J32; Secondary 35G70, 35S15.

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Coriasco, S., Schrohe, E. & Seiler, J. Realizations of Differential Operators on Conic Manifolds with Boundary. Ann Glob Anal Geom 31, 223–285 (2007). https://doi.org/10.1007/s10455-006-9019-7

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  • DOI: https://doi.org/10.1007/s10455-006-9019-7

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