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Mathematics of the USSR-Sbornik, 1970, Volume 11, Issue 3, Pages 291–309
DOI: https://doi.org/10.1070/SM1970v011n03ABEH002071
(Mi sm3453)
 

This article is cited in 8 scientific papers (total in 9 papers)

Nondegenerate subelliptic pseudodifferential operators

Yu. V. Egorov
References:
Abstract: In this paper we study scalar pseudodifferential operators for which the gradient gradx,ξp0(x,ξ) of the principal part of the symbol does not vanish and is not proportional to a real vector at any characteristic point (x,ξ)Ω×{Rn0}. Such operators are called nondegenerate. It is assumed in addition that for each point of Ω×{Rn0} there exists an operator in the Lie algebra generated by the operators P and P the principal part of the symbol of which does not vanish at this point. For these operators we present here hypoellipticity conditions, conditions for the local solvability of the equation Pu=f, a theorem on the smoothness of the solutions of this equation, and so on. All of the conditions obtained have a simple algebraic character and are exact, necessary and sufficient.
Bibliography: 13 titles.
Received: 11.06.1969
Bibliographic databases:
UDC: 517.43
Language: English
Original paper language: Russian
Citation: Yu. V. Egorov, “Nondegenerate subelliptic pseudodifferential operators”, Math. USSR-Sb., 11:3 (1970), 291–309
Citation in format AMSBIB
\Bibitem{Ego70}
\by Yu.~V.~Egorov
\paper Nondegenerate subelliptic pseudodifferential operators
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 3
\pages 291--309
\mathnet{http://mi.mathnet.ru/eng/sm3453}
\crossref{https://doi.org/10.1070/SM1970v011n03ABEH002071}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=268509}
\zmath{https://zbmath.org/?q=an:0197.40702|0216.17301}
Linking options:
  • https://www.mathnet.ru/eng/sm3453
  • https://doi.org/10.1070/SM1970v011n03ABEH002071
  • https://www.mathnet.ru/eng/sm/v124/i3/p323
  • This publication is cited in the following 9 articles:
    1. M. I. Vishik, L. R. Volevich, A. M. Il'in, A. S. Kalashnikov, V. A. Kondrat'ev, O. A. Oleinik, “Yurii Vladimirovich Egorov (on his 60th birthday)”, Russian Math. Surveys, 54:2 (1999), 465–476  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. R. S. Zolotareva, V. P. Markov, V. A. Apanas'eva, S. S. Matveichuk, Z. S. Atroshenko, “Grinding slagsitall with free abrasives”, Glass Ceram, 33:3 (1976), 197  crossref
    3. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:2 (1975), 59–118  mathnet  crossref  mathscinet  zmath
    4. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:3 (1975), 55–105  mathnet  crossref  mathscinet  zmath
    5. A. Menikoff, “Carleman estimates for partial differential operators with real coefficients”, Arch. Rational Mech. Anal., 54:2 (1974), 118  crossref
    6. L. Khermander, “O suschestvovanii i regulyarnosti reshenii lineinykh psevdodifferentsialnykh uravnenii”, UMN, 28:6(174) (1973), 109–164  mathnet  mathscinet
    7. V. V. Grushin, “Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols”, Math. USSR-Sb., 17:4 (1972), 497–514  mathnet  crossref  mathscinet  zmath
    8. Yu. V. Egorov, “On the solubility of differential equations with simple characteristics”, Russian Math. Surveys, 26:2 (1971), 113–130  mathnet  crossref  mathscinet  zmath
    9. V. V. Grushin, “On a class of hypoelliptic operators”, Math. USSR-Sb., 12:3 (1970), 458–476  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:318
    Russian version PDF:87
    English version PDF:12
    References:56
     
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