### Spectral analysis and singularities of a
noncoercive transmission problem

*Anne-Sophie Bonnet-Bendhia, Monique Dauge and Karim Ramdani*

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.