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Russian Mathematical Surveys, 1971, Volume 26, Issue 2, Pages 113–130
DOI: https://doi.org/10.1070/RM1971v026n02ABEH003823
(Mi rm5192)
 

This article is cited in 19 scientific papers (total in 20 papers)

On the solubility of differential equations with simple characteristics

Yu. V. Egorov
References:
Abstract: A survey is given of papers devoted to the problem of the existence of solutions to linear differential and pseudo-differential equations of principal type. The main results in this field are due to Lewy, Hцrmander, Nirenberg, Tréves and the author. We also give a new theorem of maximal generality on local solubility of equations of principal type. By way of illustration to the exposition we mention as examples: the Lewy operator; the operator arising from the solution of the problem with directional derivatives for elliptic second order equations; non-singular operators.
Received: 26.11.1970
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35J25, 35Sxx, 35A10
Language: English
Original paper language: Russian
Citation: Yu. V. Egorov, “On the solubility of differential equations with simple characteristics”, Russian Math. Surveys, 26:2 (1971), 113–130
Citation in format AMSBIB
\Bibitem{Ego71}
\by Yu.~V.~Egorov
\paper On the solubility of differential equations with simple characteristics
\jour Russian Math. Surveys
\yr 1971
\vol 26
\issue 2
\pages 113--130
\mathnet{http://mi.mathnet.ru/eng/rm5192}
\crossref{https://doi.org/10.1070/RM1971v026n02ABEH003823}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=296481}
\zmath{https://zbmath.org/?q=an:0213.37003}
Linking options:
  • https://www.mathnet.ru/eng/rm5192
  • https://doi.org/10.1070/RM1971v026n02ABEH003823
  • https://www.mathnet.ru/eng/rm/v26/i2/p183
  • This publication is cited in the following 20 articles:
    1. J.-A. Marti, V. Dévoué, A. Delcroix, E. Allaud, H. Vernaeve, R. Ibragimov, V. Vougalter, M.W. Wong, “On the Well-posedness of Some generalized Characteristic Cauchy Problems”, Math. Model. Nat. Phenom., 11:2 (2016), 89  crossref
    2. Guang Shan Xu, Zhong Tai Ma, “The Problem of Non-Smooth Solutions for a Type of Parabolic Complex Equations”, AMM, 40-41 (2010), 877  crossref
    3. 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
    4. Nicolas Lerner, Luc Robbiano, “Unicite de cauchy pour des operateurs de type principal par”, J Anal Math, 44:1 (1984), 32  crossref  mathscinet  isi
    5. Yu. V. Egorov, “Equations of principal type. Sufficient conditions for local solvability”, Math. USSR-Sb., 44:4 (1983), 517–525  mathnet  crossref  mathscinet  zmath
    6. Yu. V. Egorov, Ts. V. Rangelov, “Ob odnom klasse psevdodifferentsialnykh uravnenii s dvukratnymi kharakteristikami, ne imeyuschikh reshenii”, UMN, 32:1(193) (1977), 185–186  mathnet  mathscinet  zmath
    7. Yu. V. Egorov, “Novoe dokazatelstvo teoremy o lokalnoi razreshimosti uravnenii s prostymi veschestvennymi kharakteristikami”, UMN, 32:2(194) (1977), 211–212  mathnet  mathscinet  zmath
    8. N. A. Shananin, “K neobkhodimym usloviyam lokalnoi razreshimosti uravnenii kvaziglavnogo tipa”, UMN, 32:2(194) (1977), 235–236  mathnet  mathscinet  zmath
    9. G. M. Henkin, “The Lewy equation and analysis on pseudoconvex manifolds”, Russian Math. Surveys, 32:3 (1977), 59–130  mathnet  crossref  mathscinet  zmath
    10. A. M. Vinogradov, B. A. Kupershmidt, “The structures of Hamiltonian mechanics”, Russian Math. Surveys, 32:4 (1977), 177–243  mathnet  crossref  mathscinet  zmath
    11. P. R. Popivanov, “Local solvability of pseudodifferential operators with characteristics of second multiplicity”, Math. USSR-Sb., 29:2 (1976), 193–216  mathnet  crossref  mathscinet  zmath  isi
    12. N. A. Shananin, “On local solvability of equations of quasi-principal type”, Math. USSR-Sb., 26:4 (1975), 458–470  mathnet  crossref  mathscinet  zmath
    13. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:2 (1975), 59–118  mathnet  crossref  mathscinet  zmath
    14. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:3 (1975), 55–105  mathnet  crossref  mathscinet  zmath
    15. A. M. Vinogradov, I. S. Krasil'shchik, “What is the hamiltonian formalism?”, Russian Math. Surveys, 30:1 (1975), 177–202  mathnet  crossref  mathscinet  zmath
    16. L. Nirenberg, “Lektsii o lineinykh differentsialnykh uravneniyakh s chastnymi proizvodnymi”, UMN, 30:4(184) (1975), 147–204  mathnet  mathscinet  zmath
    17. P. R. Popivanov, “O razreshimosti i gipoelliptichnosti differentsialnykh uravnenii”, UMN, 29:1(175) (1974), 185–186  mathnet  mathscinet  zmath
    18. Yu. V. Egorov, P. R. Popivanov, “Equations of principal type witgout solution”, Russian Math. Surveys, 29:2 (1974), 176–194  mathnet  crossref  mathscinet  zmath
    19. P. R. Popivanov, “O lokalnoi razreshimosti psevdodifferentsialnykh uravnenii s dvukhkratnymi kharakteristikami”, UMN, 29:5(179) (1974), 233–234  mathnet  mathscinet  zmath
    20. L. Khermander, “O suschestvovanii i regulyarnosti reshenii lineinykh psevdodifferentsialnykh uravnenii”, UMN, 28:6(174) (1973), 109–164  mathnet  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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