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Mat. Sb., 1992, Volume 183, Number 1, Pages 114–129 (Mi msb1456)  

This article is cited in 2 scientific papers (total in 3 papers)

Geometry of local lacunae of hyperbolic operators with constant coefficients

V. A. Vassiliev


Abstract: 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.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 111–123

Bibliographic databases:

MSC: 35L25, 35A08
Received: 28.12.1990

Citation: V. A. Vassiliev, “Geometry of local lacunae of hyperbolic operators with constant coefficients”, Mat. Sb., 183:1 (1992), 114–129; Russian Acad. Sci. Sb. Math., 75:1 (1993), 111–123

Citation in format AMSBIB
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\by V.~A.~Vassiliev
\paper Geometry of local lacunae of hyperbolic operators with constant coefficients
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 1
\pages 114--129
\mathnet{http://mi.mathnet.ru/msb1456}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1166760}
\zmath{https://zbmath.org/?q=an:0773.35038}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..75..111V}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 111--123
\crossref{https://doi.org/10.1070/SM1993v075n01ABEH003374}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LG75100006}


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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. 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
    2. 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
    3. Victor A. Vassiliev, “New Examples of Irreducible Local Diffusion of Hyperbolic PDE's”, SIGMA, 16 (2020), 009, 21 pp.  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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