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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 2, Pages 242–283 (Mi izv1479)

Sharpness and the local Petrovskii condition for strictly hyperbolic operators with constant coefficients

V. A. Vassiliev

Abstract: It is proved that for almost all hyperbolic operators with constant coefficients analytic sharpness of the fundamental solution everywhere is equivalent to the local Petrovskii condition. In the proximity of simple ($O$-modal) singularities of wave front sets the author finds all domains from one side of which there is sharpness.
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:2, 233–273

Bibliographic databases:

UDC: 517.4
MSC: Primary 35L30; Secondary 35E15, 57R45

Citation: V. A. Vassiliev, “Sharpness and the local Petrovskii condition for strictly hyperbolic operators with constant coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 50:2 (1986), 242–283; Math. USSR-Izv., 28:2 (1987), 233–273

Citation in format AMSBIB
\Bibitem{Vas86} \by V.~A.~Vassiliev \paper Sharpness and the local Petrovskii condition for strictly hyperbolic operators with constant coefficients \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 2 \pages 242--283 \mathnet{http://mi.mathnet.ru/izv1479} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=842583} \zmath{https://zbmath.org/?q=an:0615.35012} \transl \jour Math. USSR-Izv. \yr 1987 \vol 28 \issue 2 \pages 233--273 \crossref{https://doi.org/10.1070/IM1987v028n02ABEH000880} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. N. Varchenko, “On normal forms of nonsmoothness of solutions of hyperbolic equations”, Math. USSR-Izv., 30:3 (1988), 615–628
2. V. A. Vassiliev, “Geometry of local lacunae of hyperbolic operators with constant coefficients”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 111–123
3. Dirk-J. Smit, Maarten V. Hoop, “The geometry of the hyperbolic system for an anisotropic perfectly elastic medium”, Comm Math Phys, 167:2 (1995), 255
4. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845
5. V. A. Vassiliev, “Newton's lemma XXVIII on integrable ovals in higher dimensions and reflection groups”, Bulletin of the London Mathematical Society, 2015
6. V. A. Vassiliev, “Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations”, Sb. Math., 207:10 (2016), 1363–1383
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