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Spectral analysis and singularities of a non-coercive transmission problem. (Analyse specrale et singularités d’un problème de transmission non coercif.) (French) Zbl 0932.35153
Summary: This note is devoted to the spectral analysis of an unbounded operator associated with a noncoercive transmission problem. Using an integral equation method, we show that, if the interface is regular, this operator is selfadjoint and has compact resolvent. If the interface has a corner, the study of the singularities using Mellin transform allows us to derive a necessary and sufficient condition on the contrast between the two media for selfadjointness. If the operator is not selfadjoint, a characterization of its selfadjoint extensions is given.

MSC:
35P05 General topics in linear spectral theory for PDEs
47G10 Integral operators
35B65 Smoothness and regularity of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
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