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Uspekhi Mat. Nauk, 1975, Volume 30, Issue 2(182), Pages 57–114 (Mi umn3987)  

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

Subelliptic operators

Yu. V. Egorov

Abstract: We consider a class of pseudodifferential operators that occupies an intermediate position between the classes of elliptic and hyperbolic operators. We give an adequate description of subelliptic scalar operators in terms of the highest part of the symbol. Our results can be used in the study of boundary value problems for elliptic differential equations.

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English version:
Russian Mathematical Surveys, 1975, 30:2, 59–118

Bibliographic databases:

UDC: 517.4
MSC: 35H20, 35Sxx, 47G30, 35J55, 47F05
Received: 15.06.1974

Citation: Yu. V. Egorov, “Subelliptic operators”, Uspekhi Mat. Nauk, 30:2(182) (1975), 57–114; Russian Math. Surveys, 30:2 (1975), 59–118

Citation in format AMSBIB
\by Yu.~V.~Egorov
\paper Subelliptic operators
\jour Uspekhi Mat. Nauk
\yr 1975
\vol 30
\issue 2(182)
\pages 57--114
\jour Russian Math. Surveys
\yr 1975
\vol 30
\issue 2
\pages 59--118

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    This publication is cited in the following articles:
    1. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:3 (1975), 55–105  mathnet  crossref  mathscinet  zmath
    2. A. V. Babin, “A formula expressing the solution of a differential equation with analytic coefficients on a manifold without boundary in terms of the data of the problem”, Math. USSR-Sb., 30:4 (1976), 539–563  mathnet  crossref  mathscinet  zmath  isi
    3. Yu. V. Egorov, “O gladkosti reshenii uravnenii glavnogo tipa”, UMN, 32:5(197) (1977), 183–184  mathnet  mathscinet  zmath
    4. Yu. V. Egorov, “An inequality for differential operators of the first order”, Russian Math. Surveys, 33:6 (1978), 225–226  mathnet  crossref  mathscinet  zmath
    5. C. Fefferman, D. H. Phong, “The uncertainty principle and sharp gårding inequalities”, Comm Pure Appl Math, 34:3 (1981), 285  crossref  mathscinet  zmath  isi
    6. S. E. Pastukhova, “On the well-posedness of a mixed boundary-value problem for a hyperbolic equation”, Russian Math. Surveys, 36:5 (1981), 171–172  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Ulf Pillat, Bert—Wolfgang Schulze, “Some classes of non—elliptic boundary value problems for pseudo—differential operators II. overdetermined and under— determined systems”, Communications in Partial Differential Equations, 6:4 (1981), 373  crossref
    8. Kazuaki Taira, “Un théorème d'existence et d'unicité des solutions pour des problèmes aux limites non-elliptiques”, Journal of Functional Analysis, 43:2 (1981), 166  crossref
    9. Yu. A. Dubinskii, “The algebra of pseudodifferential operators with analytic symbols and its applications to mathematical physics”, Russian Math. Surveys, 37:5 (1982), 109–153  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. V. Korenyako, “The Gárding inequality for a system of pseudodifferential operators”, Russian Math. Surveys, 38:1 (1983), 198–199  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Jean-Marie Trepeau, “Sur l'hypoellipticite analytique microlocale des operateurs de type principal”, Communications in Partial Differential Equations, 9:11 (1984), 1119  crossref
    12. T. V. Gramchev, P. R. Popivanov, “Microlocal properties of the problem with a singular oblique derivative in a neighbourhood of diffractive points”, Russian Math. Surveys, 41:1 (1986), 223–224  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. Charles Rockland, “Intrinsic nilpotent approximation”, Acta Appl Math, 8:3 (1987), 213  crossref  mathscinet  zmath  isi
    14. Jean Nourrigat, “Inégalités L2 et représentations de groupes nilpotents”, Journal of Functional Analysis, 74:2 (1987), 300  crossref
    15. J. Nurrigat, “Subelliptic systems”, Communications in Partial Differential Equations, 15:3 (1990), 341  crossref
    16. A. P. Fordy, A. B. Shabat, A. P. Veselov, “Factorization and Poisson correspondences”, Theoret. and Math. Phys., 105:2 (1995), 1369–1386  mathnet  crossref  mathscinet  zmath  isi  elib
    17. Vladimir Tulovsky, “On an interpretation of Hörmander's condition of local solvability”, Indagationes Mathematicae, 9:1 (1998), 123  crossref
    18. 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
    19. V. V. Ryzhikov, S. V. Tikhonov, “Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions”, Math. Notes, 79:6 (2006), 864–868  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. Marco Mughetti, “Regularity properties of a double characteristics differential operator with complex lower order terms”, J. Pseudo-Differ. Oper. Appl, 2014  crossref
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