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.
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To Professor Georgii S. Litvinchuk on the occasion of his 70th birthday
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Castro, L.P., Duduchava, R., Speck, FO. (2003). Localization and Minimal Normalization of Some Basic Mixed Boundary Value Problems. In: Samko, S., Lebre, A., dos Santos, A.F. (eds) Factorization, Singular Operators and Related Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0227-0_7
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DOI: https://doi.org/10.1007/978-94-017-0227-0_7
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