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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 1(5), Pages 18–48 (Mi msb3180)  

This article is cited in 13 scientific papers (total in 13 papers)

On a criterion for hypoellipticity

V. S. Fedii

Abstract: In this paper a criterion for hypoellipticity is proved which is formulated in terms of certain estimates in the $H_{(s)}$ norms, and which is a generalization of a criterion of Trèves. With the use of this criterion it is possible to prove the hypoellipticity of certain operators that do not satisfy Hörmander's criterion. It is proved, for example, that the operator $P=\partial^2/\partial x^2+\varphi^2(x)\partial^2/\partial y^2$ is hypoelliptic, where $\varphi(x)$ is an infinitely differentiable function that is not equal to zero for $x\ne0$ and has a zero of infinite order at $x=0$.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:1, 15–45

Bibliographic databases:

UDC: 517.43
MSC: 47F05
Received: 17.04.1970

Citation: V. S. Fedii, “On a criterion for hypoellipticity”, Mat. Sb. (N.S.), 85(127):1(5) (1971), 18–48; Math. USSR-Sb., 14:1 (1971), 15–45

Citation in format AMSBIB
\by V.~S.~Fedii
\paper On a~criterion for hypoellipticity
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 1(5)
\pages 18--48
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 1
\pages 15--45

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    This publication is cited in the following articles:
    1. 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
    2. Kazuo Amano, “Hypoellipticity of a class of degenerate elliptic–parabolic operators”, Communications in Partial Differential Equations, 6:8 (1981), 903  crossref  mathscinet  zmath
    3. Osamu Kobayashi, Akira Yoshioka, Yoshiaki Maeda, Hideki Omori, “The theory of infinite-dimensional Lie groups and its applications”, Acta Appl Math, 3:1 (1985), 71  crossref  mathscinet  zmath
    4. Toshihiko Hoshiro, “On Levi-type conditions for hypoellipticity of certain diffrential operators”, Communications in Partial Differential Equations, 17:5-6 (1992), 905  crossref  mathscinet  zmath
    5. G. A. Smolkin, “On a property of solutions of a special class of degenerate elliptic equations”, Russian Math. Surveys, 51:3 (1996), 561–562  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Nguyen Minh Tri, “On Grushin's equation”, Math. Notes, 63:1 (1998), 84–93  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. J.J Kohn, “Hypoellipticity of Some Degenerate Subelliptic Operators”, Journal of Functional Analysis, 159:1 (1998), 203  crossref  mathscinet  zmath
    8. Nguyen Minh Tri, “Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators”, Math. Notes, 71:4 (2002), 517–529  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Eric T. Sawyer, Richard L. Wheeden, “ A priori estimates for quasilinear equations related to the Monge-Ampère equation in two dimensions”, J Anal Math, 97:1 (2005), 257  crossref  mathscinet  isi
    10. Luca Baracco, Tran Vu Khanh, Giuseppe Zampieri, “Propagation of holomorphic extendibility and non-hypoellipticity of the -Neumann problem in an exponentially degenerate boundary”, Advances in Mathematics, 230:4-6 (2012), 1972  crossref  mathscinet  zmath
    11. Cristian Rios, E.T.. Sawyer, R.L.. Wheeden, “Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem”, JAMA, 119:1 (2013), 1  crossref  mathscinet  zmath
    12. Lyudmila Korobenko, Cristian Rios, “Hypoellipticity of certain infinitely degenerate second order operators”, Journal of Mathematical Analysis and Applications, 2013  crossref  mathscinet
    13. Luca Baracco, “A multiplier condition for hypoellipticity with optimal loss of derivatives of complex vector fields”, Journal of Mathematical Analysis and Applications, 2014  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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