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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.

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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