Skip to main content
Log in

Systems of differential operators in anisotropic Roumieu classes

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

The aim of this work is to show that the ellipticity is a sufficient condition for the elliptic iterate property to hold for systems of linear differential operators in the anisotropic Roumieu classes.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bolley, P., Camus, J.: Powers and Gevrey regularity for a system of differential operators. Czechoslovak Math. J., Praha 29(104), 649–661 (1979)

    MathSciNet  Google Scholar 

  2. Bouzar, C., Chaïli, R.: Régularité des vecteurs de Beurling de systèmes elliptiques. Maghreb Math. Rev. 9(1–2), 43–53 (2000)

    MathSciNet  Google Scholar 

  3. Bouzar, C., Chaïli, R.: Une généralisation de la propriété des itérés. Archiv Math. 76(1), 57–66 (2001)

    Article  MATH  Google Scholar 

  4. Bouzar, C., Chaïli, R.: Vecteurs Gevrey d’opérateurs différentiels quasihomogènes. Bull. Belgian Math. Soc. 9(2), 299–310 (2002)

    MATH  Google Scholar 

  5. Chaïli R.: Beurling vectors of quasielliptic systems of differential operators. J Inequal. Pure Appl. Math. 4(5), Article 85 (2003)

    Google Scholar 

  6. John O.: Sulla regolarità delle soluzioni delle equazioni lineari ellittiche nelle classi di Beurling. Boll. U.M.I. 4(2), 183–195 (1969)

    Google Scholar 

  7. Juan-Huguet, J.: Iterates and hypoellipticity of partial differential operators on non-quasianalytic classes. Integr. Equ. Oper. Theory. 68, 263–286 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Komatsu, H.: A characterization of real Analytic functions. Proc. Jpn Acad. 36, 90–93 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kotake, T., Narasimhan, M.S.: Regularity theorems for fractional powers of a linear elliptic operator. Bull. Soc. Math. France 90, 449–471 (1962)

    MathSciNet  MATH  Google Scholar 

  10. Lions, J.L., Magenes, E.: Problèmes aux limites non homogenes et appliquations, vol. 3. Dunod, Paris (1970)

    Google Scholar 

  11. Métivier, G.: Propriété des itérés et ellipticité. Comm. Partial. Differ. Equ. 9(3), 827–876 (1978)

    Article  Google Scholar 

  12. Newberger, E., Zielezny, Z.: The growth of hypoelliptic polynomials and Gevrey classes. Proc. Am. Math. Soc. 39, 547–552 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zanghirati, L.: Iterati di operatori quasi-ellittici e classi di Gevrey. Bollettino U.M.I. 5(18–B), 411–428 (1981)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rachid Chaili.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chaili, R. Systems of differential operators in anisotropic Roumieu classes. Rend. Circ. Mat. Palermo 62, 189–198 (2013). https://doi.org/10.1007/s12215-012-0101-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-012-0101-7

Keywords

Mathematics Subject Classification (2000)

Navigation