This Note is devoted to the spectral analysis of an unbounded operator associated with a non coercive 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.
Note C. R. Acad. Sc. Paris Série I, 328, 1999, 717--720.
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