Geodesic
Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II
Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 205-231 
I. V. Kamotskii; S. A. Nazarov. Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II. Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 205-231. http://geodesic.mathdoc.fr/item/SM_1999_190_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The solution of the problem of diffraction of an acoustic plane wave by a periodic boundary for frequencies close to threshold values is studied. It is shown that if the periodic structure has some special geometry, then the transformations of the diffraction pattern (Wood's anomalies) are accompanied by the occurrence of surface waves. Substantiation of asymptotic formulae (in particular, the ones in [1]) is carried out on the basis of the techniques of equivalent weighted norms in Sobolev spaces.

[1] Kamotskii I. V., Nazarov S. A., “Anomalii Vuda i poverkhnostnye volny v zadache rasseyaniya na periodicheskoi granitse, I”, Matem. sb., 190:1 (1998), 109–138 | MR

[2] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16, URSS, M., 1967, 209–292 | MR | Zbl

[3] Mazja W. G., Nasarov S. A., Plamenewski B. A., Asymptotishe Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, V. 1, Akademie-Verlag, Berlin, 1990

[4] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[5] Babich V. M., “O teoreme suschestvovaniya resheniya zadach Dirikhle i Neimana dlya uravneniya Gelmgoltsa v kvaziperiodicheskom sluchae”, Sib. matem. zhurn., 29:2 (1988), 3–9 | MR

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

[7] Nasarov S. A., Plamenewski B. A., Elliptic problems in domains with piecewise smooth boundaries, Walter de Gruyter, Berlin, 1994 | MR

[8] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991