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

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

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
\Bibitem{Ego75} \by Yu.~V.~Egorov \paper Subelliptic operators \jour Uspekhi Mat. Nauk \yr 1975 \vol 30 \issue 2(182) \pages 57--114 \mathnet{http://mi.mathnet.ru/umn3987} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=410473} \zmath{https://zbmath.org/?q=an:0309.35067|0318.35075} \transl \jour Russian Math. Surveys \yr 1975 \vol 30 \issue 2 \pages 59--118 \crossref{https://doi.org/10.1070/RM1975v030n02ABEH001407} 

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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. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:3 (1975), 55–105
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
3. Yu. V. Egorov, “O gladkosti reshenii uravnenii glavnogo tipa”, UMN, 32:5(197) (1977), 183–184
4. Yu. V. Egorov, “An inequality for differential operators of the first order”, Russian Math. Surveys, 33:6 (1978), 225–226
5. C. Fefferman, D. H. Phong, “The uncertainty principle and sharp gårding inequalities”, Comm Pure Appl Math, 34:3 (1981), 285
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
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
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
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
10. V. V. Korenyako, “The Gárding inequality for a system of pseudodifferential operators”, Russian Math. Surveys, 38:1 (1983), 198–199
11. Jean-Marie Trepeau, “Sur l'hypoellipticite analytique microlocale des operateurs de type principal”, Communications in Partial Differential Equations, 9:11 (1984), 1119
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
13. Charles Rockland, “Intrinsic nilpotent approximation”, Acta Appl Math, 8:3 (1987), 213
14. Jean Nourrigat, “Inégalités L2 et représentations de groupes nilpotents”, Journal of Functional Analysis, 74:2 (1987), 300
15. J. Nurrigat, “Subelliptic systems”, Communications in Partial Differential Equations, 15:3 (1990), 341
16. A. P. Fordy, A. B. Shabat, A. P. Veselov, “Factorization and Poisson correspondences”, Theoret. and Math. Phys., 105:2 (1995), 1369–1386
17. Vladimir Tulovsky, “On an interpretation of Hörmander's condition of local solvability”, Indagationes Mathematicae, 9:1 (1998), 123
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
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
20. Marco Mughetti, “Regularity properties of a double characteristics differential operator with complex lower order terms”, J. Pseudo-Differ. Oper. Appl, 2014
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