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

This article is cited in 5 scientific papers (total in 6 papers)

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
Received: 27.02.1984

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
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  mathscinet  zmath
    2. V. A. Vassiliev, “Geometry of local lacunae of hyperbolic operators with constant coefficients”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 111–123  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  crossref  mathscinet  zmath
    4. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. V. A. Vassiliev, “Newton's lemma XXVIII on integrable ovals in higher dimensions and reflection groups”, Bulletin of the London Mathematical Society, 2015  crossref
    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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