Localization and Minimal Normalization of Some Basic Mixed Boundary Value Problems

Luís P. Castro (), Roland Duduchava () and Frank-Olme Speck ()
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Luís P. Castro: University of Aveiro
Roland Duduchava: A. Razmadze Mathematical Institute
Frank-Olme Speck: Technical University of Lisbon, Instituto Superior Técnico

A chapter in Factorization, Singular Operators and Related Problems, 2003, pp 73-100 from Springer

Abstract: 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.

Keywords: Normalization; boundary value problems; localization; pseudo-differential operators; Wiener-Hopf operators; Fredholm property; Bessel potential spaces. (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0227-0_7

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DOI: 10.1007/978-94-017-0227-0_7

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