Geodesic
Geometry of local lacunae of hyperbolic operators with constant coefficients
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 111-123 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A graphical geometric characterization is given of local lacunae (domains of regularity of the fundamental solution) near the simple singular points of the wave fronts of nondegenerate hyperbolic operators. To wit: a local (near a simple singularity of the front) component of the complement of the front is a local lacuna precisely when it satisfies the Davydov–Borovikov signature condition near all the nonsingular points on its boundary, and its boundary has no edges of regression near which the component in question is a “large” component of the complement of the front. 
@article{SM_1993_75_1_a5,
     author = {V. A. Vassiliev},
     title = {Geometry of local lacunae of hyperbolic operators with constant coefficients},
     journal = {Sbornik. Mathematics},
     pages = {111--123},
     year = {1993},
     volume = {75},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_75_1_a5/}
}
TY  - JOUR
AU  - V. A. Vassiliev
TI  - Geometry of local lacunae of hyperbolic operators with constant coefficients
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 111
EP  - 123
VL  - 75
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1993_75_1_a5/
LA  - en
ID  - SM_1993_75_1_a5
ER  - 
%0 Journal Article
%A V. A. Vassiliev
%T Geometry of local lacunae of hyperbolic operators with constant coefficients
%J Sbornik. Mathematics
%D 1993
%P 111-123
%V 75
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1993_75_1_a5/
%G en
%F SM_1993_75_1_a5
V. A. Vassiliev. Geometry of local lacunae of hyperbolic operators with constant coefficients. Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 111-123. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a5/

[1] Arnold V. I., “Normalnye formy funktsii vblizi vyrozhdennykh kriticheskikh tochek”, Funktsion. analiz i ego pril., 6:4 (1972), 3–25 | MR

[2] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. I. Klassifikatsiya kriticheskikh tochek, kaustik, i volnovykh frontov, Nauka, M., 1982 | MR

[3] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. II. Monodromiya i asimptotiki integralov, Nauka, M., 1984 | MR

[4] Arnold V. I., Vasilev V. A., Goryunov V. V., Lyashko O. V., Osobennosti. I. Lokalnaya i globalnaya teoriya, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 6, VINITI, M., 1988 | MR

[5] Arnold V. I., Vasilev V. A., Goryunov V. V., Lyashko O. V., Osobennosti. II. Klassifikatsiya i prilozheniya, Sovremennye problemy matematiki. Fundamentalnye napravleniya. Itogi nauki i tekhniki, 39, VINITI, M., 1989 | MR

[6] Atya M. F., Bott R., Gording L., “Lakuny dlya giperbolicheskikh differentsialnykh operatorov s postoyannymi koeffitsientami. I, II”, UMN, 26:2 (1971), 25–100 ; 39:2 (1984), 171–224 | MR | MR

[7] Borovikov V. A., “Fundamentalnye resheniya lineinykh uravnenii v chastnykh proizvodnykh”, Tr. MMO, 8 (1959), 199–257 | MR

[8] Davydova A. M., Dostatochnoe uslovie otsutstviya lakuny dlya differentsialnogo uravneniya v chastnykh proizvodnykh giperbolicheskogo tipa, Dis. ... k-ta fiz.-mat. nauk, MGU, M., 1945, 43 pp.

[9] Gording L., “Rezkie fronty parnykh ostsilliruyuschikh integralov”, UMN, 38:6 (1983), 85–96 | MR

[10] Gusein-Zade S. M., “Matritsy peresechenii dlya nekotorykh osobennostei funktsii dvukh peremennykh”, Funktsion. analiz i ego pril., 8:1 (1974), 11–15 | MR | Zbl

[11] Khermander L., “Integralnye operatory Fure, I”, Matematika, 16:1 (1972), 17–61 | Zbl

[12] Lere Zh., Obobschennoe preobrazovanie Laplasa, Mir, M., 1969 | MR

[13] Lyashko O. V., “Raspadeniya prostykh osobennostei funktsii”, Funktsion. analiz i ego pril., 10:2 (1976), 49–56 | Zbl

[14] Looijenga E., “The complement of the bifurcation variety of a simple singularity”, Invent. Math., 23 (1974), 105–116 | DOI | MR | Zbl

[15] Looijenga E., “The discriminant of a real simple singularity”, Compositio Math., 37 (1978), 51–62 | MR | Zbl

[16] Milnor Dzh., Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[17] Petrovskii I. G., “On the diffusion of waves and the lacunas for hyperbolic equations”, Matem. sb., 17 (59):3 (1945), 289–370 | MR

[18] Vasilev V. A., “Rezkost i lokalnoe uslovie Petrovskogo dlya strogo giperbolicheskikh operatorov s postoyannymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 50:2 (1986), 242–283 | MR

[19] Vassilyev V. A., Lagrange and Legendre characteristic classes, Gordon Breach, New York a. o., 1988 | MR | Zbl

[20] Zakalyukin V. M., “O lagranzhevykh i lezhandrovykh osobennostyakh”, Funktsion. analiz i ego pril., 10:1 (1976), 26–36 | MR | Zbl