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Localization and Minimal Normalization of Some Basic Mixed Boundary Value Problems

In: Factorization, Singular Operators and Related Problems

Author

Listed:
  • Luís P. Castro

    (University of Aveiro)

  • Roland Duduchava

    (A. Razmadze Mathematical Institute)

  • Frank-Olme Speck

    (Technical University of Lisbon, Instituto Superior Técnico)

Abstract

We consider a class of mixed boundary value problems in spaces of Bessel potentials. By localization, an operator L associated with the BVP is related through operator matrix identities to a family of pseudodifferential operators which leads to a Fredholm criterion for L. But particular attention is devoted to the non-Fredholm case where the image of L is not closed. Minimal normalization, which means a certain minimal change of the spaces under consideration such that either the continuous extension of L or the image restriction, respectively, is normally solvable, leads to modified spaces of Bessel potentials. These can be characterized in a physically relevant sense and seen to be closely related to operators with transmission property (domain normalization) or to problems with compatibility conditions for the data (image normalization), respectively.

Suggested Citation

  • Luís P. Castro & Roland Duduchava & Frank-Olme Speck, 2003. "Localization and Minimal Normalization of Some Basic Mixed Boundary Value Problems," Springer Books, in: Stefan Samko & Amarino Lebre & António F. dos Santos (ed.), Factorization, Singular Operators and Related Problems, pages 73-100, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0227-0_7
    DOI: 10.1007/978-94-017-0227-0_7
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