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

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

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
\Bibitem{Vas92} \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
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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
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
3. Victor A. Vassiliev, “New Examples of Irreducible Local Diffusion of Hyperbolic PDE's”, SIGMA, 16 (2020), 009, 21 pp.
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