Skip to main content
SpringerLink
Log in

The local real analyticity of solutions to □ b and the \(\bar \partial \)-Neumann problem

  • Published:
Acta Mathematica

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. Agmon, S., Douglis, A. &Nirenberg,L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, IComm. Pure Appl. Math., 12 (1959), 623–727; II,ibid., 17 (1964), 35–92.

    Article  MATH  MathSciNet  Google Scholar 

  2. Ash, M. E., The basic estimate of the\(\bar \partial \)-Neumannn problem in the non-Kählerian case.Amer. J. Math., 86 (1964), 247–254.

    Article  MATH  MathSciNet  Google Scholar 

  3. Baouendi, M. S. &Goulaouic, C., Analyticity for degenerate elliptic equations and applications.Proc. Symposia in Pure Math., 23 (1971), 79–84.

    Google Scholar 

  4. Boutet De Monvel, L., Comportement d'un opérateur pseudo-differentiel sur une variété à bord, I, II.,J. Anal. Math., 17 (1966), 241–304.

    Article  MathSciNet  Google Scholar 

  5. Conner, P. E., The Neumann's problem for differential forms on Riemannian manifolds.Mem. Amer. Math. Soc., 20, 1956.

  6. Derridj, M., Sur la régularité Gevrey jusqu'au bord des solutions du problème de Neumann pour\(\bar \partial \).Proc. Symposia in Pure Math., 30:1 (1977), 123–126.

    MathSciNet  Google Scholar 

  7. Derridj, M. &Tartakoff, D. S., On the global real analyticity of solutions to the\(\bar \partial \)-Neumann problem.Comm. Partial Differential Equations, 1 (1976), 401–435.

    Article  MATH  MathSciNet  Google Scholar 

  8. Derridj, M. & Tartakoff, D. S. Sur la régularité locale des solutions du problème de Neumann pour\(\bar \partial \).Journées sur les fonctions analytiques, in Springer Lecture Notes in Math., 578, 1977, 207–216.

  9. Dynin, A., Pseudodifferential operators on Heisenberg groups. To appear.

  10. Folland, G. B. & Kohn, J. J.,The Neumann Problem for the Cauchy-Riemann Complex. Annals of Math. Studies Number 75, Princeton, 1972.

  11. Folland, G. B. &Stein, E. M., Estimates for the\(\bar \partial _b \) complex and analysis on the Heisenberg group.Comm. Pure Appl. Math., 27 (1974), 429–522.

    Article  MATH  MathSciNet  Google Scholar 

  12. Garabedian, P. &Spencer, D. C., Complex boundary value problems.Trans. Amer. Math. Soc., 73 (1952), 223–242.

    Article  MATH  MathSciNet  Google Scholar 

  13. Greiner, P. C. & Stein, E. M., Estimates for the\(\bar \partial \)-Neumann Problem Princeton, 1977.

  14. Hörmander, L., Fourier integral operators, I.,Acta Math., 128 (1971), 79–183.

    Article  Google Scholar 

  15. —,Linear partial Differential Operators. Springer Verlag, New York, 1963.

    MATH  Google Scholar 

  16. —, Pseudo-differential operators and non-elliptic boundary problems.Ann. of Math., 83 (1966), 129–209.

    Article  MathSciNet  Google Scholar 

  17. —,An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966.

    MATH  Google Scholar 

  18. Kohn, J. J., Harmonic integrals on strongly pseudoconvex manifolds, I.Ann. of Math., 78 (1963), 112–148; II,Ibid., 79 (1964), 450–472.

    Article  MathSciNet  Google Scholar 

  19. —, Boundaries of complex manifolds.Proc. Conf. on Complex Manifolds (Minneapolis), Springer-Verlag, New York, 1965.

    Google Scholar 

  20. Kohn, J. J. &Nirenberg L., Non-coercive boundary value problems.Comm. Pure Appl. Math., 18 (1965), 443–492.

    Article  MATH  MathSciNet  Google Scholar 

  21. Kohn, J. J. &Spencer, D. C., Complex Neumann problems.Ann. of Math., 66 (1957), 89–140.

    Article  MathSciNet  Google Scholar 

  22. Komatsu, G., Global analytic-hypoellipticity of the\(\bar \partial \)-Neuman problemTôhoku Math. J. Ser. 2, 28 (1976), 145–156.

    Article  MATH  MathSciNet  Google Scholar 

  23. Morrey, C. B. &Nirenberg, L., On the analyticity of the solutions of linear elliptic systems of partial differential equations.Comm. Pure Appl. Math., 10 (1957), 271–290.

    Article  MATH  MathSciNet  Google Scholar 

  24. Nirenberg, L.,Lectures on Partial Differential Equations. Texas Technical Univ., Lubbock, 1972.

    Google Scholar 

  25. Sato, M., Kawai, T. & Kashiwara, M.,Microfunction and Pseudo-differential Equations. Lecture notes in Mathematics 287, Springe 1973, 265–529.

  26. Tartakoff, D. S., Gevrey hypoellipticity for subelliptic boundary value problems.Comm. Pure Appl. Math., 26 (1973), 251–312.

    Article  MATH  MathSciNet  Google Scholar 

  27. —, On the global real analyticity of solutions to □ b .Comm. Partial Differential Equations 1 (1976), 283–311.

    Article  MathSciNet  Google Scholar 

  28. —, Local Gevrey and quasianalytic hypoellipticity for □ b .Bull. Amer. Math. Soc., 82 (1976), 740–742.

    Article  MATH  MathSciNet  Google Scholar 

  29. Tartakoff, D. S., Remarks on the intersection of certain quasianalytic classes and the quasianalytic hypoellipticity of □ b To appear.

  30. —, Local analytic hypoellipticity for □ b on non-degenerate Cauchy-Riemann manifolds.Proc. Nat. Acad. Sci. U.S.A., 75:7 (1978), 3027–3028.

    Article  MATH  MathSciNet  Google Scholar 

  31. Trèves, F., Analytic hypo-ellipticity of a class of peudodifferential operators with double characteristics and applications to the\(\bar \partial \)-Neumann problem.Comm. Partial Differential Equations, 3:6–7 (1978), 475–642.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Illinois at Chicago Circle, Chicago, Illinois, U.S.A.

    David S. Tartakoff

Authors
  1. David S. Tartakoff
    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

Tartakoff, D.S. The local real analyticity of solutions to □ b and the \(\bar \partial \)-Neumann problem. Acta Math. 145, 177–204 (1980). https://doi.org/10.1007/BF02414189

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02414189

Keywords

Search

Navigation