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Symbolic calculus for boundary value problems on manifolds with edges

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Abstract

Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbolic structure is responsible for ellipticity and for the nature of parametrices within an algebra of “edge-degenerate” pseudo-differential operators. The edge symbolic component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operator-valued Mellin symbols. We establish a calculus in a framework of “twisted homogeneity” that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute, Academy of Sciences of Georgia, 1, M. Alexidze Str., Tbilisi 93, Georgia

    D. Kapanadze

  2. Institut für Mathematik, UniversitÄt Potsdam, Postfach 601553, 14415, Potsdam, Germany

    B.-W. Schulze

Authors
  1. D. Kapanadze
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  2. B.-W. Schulze
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Kapanadze, D., Schulze, BW. Symbolic calculus for boundary value problems on manifolds with edges. Integr equ oper theory 45, 64–104 (2003). https://doi.org/10.1007/BF02789594

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