Skip to main content
SpringerLink
Log in

On degenerate elliptic operators of infinite type

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Baouendi, M.S., Goulaouic, C.: Nonanalytic-hypoellipticity for some degenerate elliptic operators, Bull. AMS78 (1972), 483–486

    MATH  MathSciNet  Google Scholar 

  2. Bergamasco, A.P., Cordaro, P.D., Malagutti, P.A.: Globally hypoelliptic systems of vector fields, Journal of Functional Analysis114, No. 2 (1993), 267–285

    Article  MATH  MathSciNet  Google Scholar 

  3. Christ, M.: Certain sums of squares of vector fields fail to be analytic hypoelliptic, Comm. Partial Differential Equations16 (1991), 1695–1707

    MATH  MathSciNet  Google Scholar 

  4. Christ, M.: A class of hypoelliptic PDE admitting nonanalytic solutions. Contemporary Mathematics, AMS137 (1992), 155–167

    MathSciNet  Google Scholar 

  5. Cordaro, P.D., Himonas, A.A.: Global analytic hypoellipticity for a class of degenerate elliptic operators on the tours, Mathematical Research Letters1, No.4 (1994), 501–510

    MATH  MathSciNet  Google Scholar 

  6. Fedii, V.S.: Estimates inH s norms and hypoellipticity, Dokl. Akad. Nauk SSSR,193, No. 2 (1970), 940–942

    MathSciNet  Google Scholar 

  7. Fefferman, C., Phong, D.: Subelliptic eigenvalue problems, Conf. on Harmonic analysis in honor of A. Zygmund, ed. by Beckner et al., Wadsworth Intern. Math. Series, Wadsworth, Belmont (1981), 590–606.

  8. Greenfield, S.J., Wallach, N.R.: Global hypoelliptic and Liouville numbers, Proceedings of the AMS31 (1972), 112–114

    Article  MATH  MathSciNet  Google Scholar 

  9. Hanges, N., Himonas, A.A.: Singular solutions for sums of squares of vector fields, Comm. Partial Differential Equations16 (8, 9) (1991), 1503–1511

    MathSciNet  Google Scholar 

  10. Hanges, N., Himonas, A.A.: Analytic hypoellipticity for generalized Baouendi-Goulaouic operators, Journal of Functional Analysis125, No. 1 (1994), 309–324

    Article  MATH  MathSciNet  Google Scholar 

  11. Hörmander, L.: Hypoelliptic second order differential equations, Acta Math.119 (1967), 147–171

    Article  MATH  MathSciNet  Google Scholar 

  12. Kohn, J.J.: Pseudo-differential operators and hypoellipticity, Proceedings of symposia in pure mathematics,XXIII (1973), 61–70

    MathSciNet  Google Scholar 

  13. Kusuoka, S., Strook, D.: Applications of the Malliavin calculus, Part II, J. Fac. Sci. Tokio, Sect IA, Math.32 (1985), 1–76

    MATH  Google Scholar 

  14. Oleinik, O.A., Radkevic, E.V.: Second order equations with nonnegative characteristic form, AMS and Plenum Press 1973

  15. Rothschild, L.P., Stein, E.M.: Hypoelliptic differential operators and nilpotent groups, Acta Math.137 (1977), 247–320

    Article  MATH  MathSciNet  Google Scholar 

  16. Sussmann, H.J.: Orbits of families of vector fields and integrability of distributions, Transactions of the AMS180 (1973), 171–188

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, 46556, Notre Dame, IN, USA

    A. Alexandrou Himonas

Authors
  1. A. Alexandrou Himonas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author was partially supported by NSF Grant DMS 91-01161

Rights and permissions

Reprints and permissions

About this article

Cite this article

Himonas, A.A. On degenerate elliptic operators of infinite type. Math Z 220, 449–460 (1995). https://doi.org/10.1007/BF02572625

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02572625

Keywords

Search

Navigation