Skip to main content
SpringerLink
Log in

Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators

Mathematical Notes volume 71, pages 517–529 (2002)Cite this article

Abstract

This paper contains examples of nonhypoelliptic infinitely degenerate elliptic differential operators. Global nonsmooth solutions of the corresponding homogeneous equations are constructed.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

REFERENCES

  1. T. Hoshiro, “Some examples of hypoelliptic operators of infinitely degenerate type,” Osaka J. Math., 30 (1993), 771–782.

    Google Scholar 

  2. M. Reissig and K. Yagdjan, “An interesting connection between hypoellipticity and branching phenomena for certain differential operators with degeneracy of infinite order,” Rend. Mat. Appl. (7), 15 (1995), 481–510.

    Google Scholar 

  3. N. M. Tri, “Non-smooth solutions for a class of infinitely degenerate elliptic differential operators,” Vietnam J. Math., 28 (2000), 159–172.

    Google Scholar 

  4. A. Gilioli and F. Treves, “An example in the solvability theory of linear PDEs,” Amer. J. Math., 96 (1974), 367–385.

    Google Scholar 

  5. A. Menikoff, “Some examples of hypoelliptic partial differential equations,” Math. Ann., 221 (1976), 176–181.

    Google Scholar 

  6. B. Helffer and L. Rodino, “Opérateurs diff´erentiels ordinaires intervenant dans l'étude de l'hypoellipticité,” Boll. U.M.I., 14-B(5) (1977), 491–522.

    Google Scholar 

  7. N. M. Tri, “Remark on non-uniform fundamental solutions and non-smooth solutions of a class of differential operators with double characteristics,” J. Math. Sci. Univ. Tokyo, 6 (1999), 437–452.

    Google Scholar 

  8. N. M. Tri, “Note on necessary conditions of hypoellipticity of some classes of differential operators with double characteristics,” Kodai Math. J., 23 (2000), 281–297.

    Google Scholar 

  9. V. S. Fedii, “On a condition of hypoellipticity,” Mat. Sb. [Math. USSR-Sb.], 85 (1971), 18–48.

    Google Scholar 

  10. Y. Morimoto and T. Morioka, “The positivity of Schrödinger operators and the hypoellipticity of second-order degenerate elliptic operators,” Bull. Sci. Math., 121 (1997), 507–547.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hanoi Institute of Mathematics, Vietnam

    Nguen Min' Tri

Authors
  1. Nguen Min' Tri
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tri, N.M. Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators. Mathematical Notes 71, 517–529 (2002). https://doi.org/10.1023/A:1014883832119

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014883832119

search

Navigation