Acta Mathematica

, Volume 145, Issue 1, pp 177–204

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

  • David S. Tartakoff


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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.MATHCrossRefMathSciNetGoogle Scholar
  2. [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.MATHCrossRefMathSciNetGoogle Scholar
  3. [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. [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.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Conner, P. E., The Neumann's problem for differential forms on Riemannian manifolds.Mem. Amer. Math. Soc., 20, 1956.Google Scholar
  6. [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.MathSciNetGoogle Scholar
  7. [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.MATHCrossRefMathSciNetGoogle Scholar
  8. [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.Google Scholar
  9. [9]
    Dynin, A., Pseudodifferential operators on Heisenberg groups. To appear.Google Scholar
  10. [10]
    Folland, G. B. & Kohn, J. J.,The Neumann Problem for the Cauchy-Riemann Complex. Annals of Math. Studies Number 75, Princeton, 1972.Google Scholar
  11. [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.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Garabedian, P. &Spencer, D. C., Complex boundary value problems.Trans. Amer. Math. Soc., 73 (1952), 223–242.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Greiner, P. C. & Stein, E. M., Estimates for the\(\bar \partial \)-Neumann Problem Princeton, 1977.Google Scholar
  14. [14]
    Hörmander, L., Fourier integral operators, I.,Acta Math., 128 (1971), 79–183.CrossRefGoogle Scholar
  15. [15]
    —,Linear partial Differential Operators. Springer Verlag, New York, 1963.MATHGoogle Scholar
  16. [16]
    —, Pseudo-differential operators and non-elliptic boundary problems.Ann. of Math., 83 (1966), 129–209.CrossRefMathSciNetGoogle Scholar
  17. [17]
    —,An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966.MATHGoogle Scholar
  18. [18]
    Kohn, J. J., Harmonic integrals on strongly pseudoconvex manifolds, I.Ann. of Math., 78 (1963), 112–148; II,Ibid., 79 (1964), 450–472.CrossRefMathSciNetGoogle Scholar
  19. [19]
    —, Boundaries of complex manifolds.Proc. Conf. on Complex Manifolds (Minneapolis), Springer-Verlag, New York, 1965.Google Scholar
  20. [20]
    Kohn, J. J. &Nirenberg L., Non-coercive boundary value problems.Comm. Pure Appl. Math., 18 (1965), 443–492.MATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    Kohn, J. J. &Spencer, D. C., Complex Neumann problems.Ann. of Math., 66 (1957), 89–140.CrossRefMathSciNetGoogle Scholar
  22. [22]
    Komatsu, G., Global analytic-hypoellipticity of the\(\bar \partial \)-Neuman problemTôhoku Math. J. Ser. 2, 28 (1976), 145–156.MATHMathSciNetCrossRefGoogle Scholar
  23. [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.MATHCrossRefMathSciNetGoogle Scholar
  24. [25]
    Nirenberg, L.,Lectures on Partial Differential Equations. Texas Technical Univ., Lubbock, 1972.Google Scholar
  25. [26]
    Sato, M., Kawai, T. & Kashiwara, M.,Microfunction and Pseudo-differential Equations. Lecture notes in Mathematics 287, Springe 1973, 265–529.Google Scholar
  26. [27]
    Tartakoff, D. S., Gevrey hypoellipticity for subelliptic boundary value problems.Comm. Pure Appl. Math., 26 (1973), 251–312.MATHCrossRefMathSciNetGoogle Scholar
  27. [28]
    —, On the global real analyticity of solutions to □b.Comm. Partial Differential Equations 1 (1976), 283–311.CrossRefMathSciNetGoogle Scholar
  28. [29]
    —, Local Gevrey and quasianalytic hypoellipticity for □b.Bull. Amer. Math. Soc., 82 (1976), 740–742.MATHMathSciNetCrossRefGoogle Scholar
  29. [30]
    Tartakoff, D. S., Remarks on the intersection of certain quasianalytic classes and the quasianalytic hypoellipticity of □b To appear.Google Scholar
  30. [31]
    —, Local analytic hypoellipticity for □b on non-degenerate Cauchy-Riemann manifolds.Proc. Nat. Acad. Sci. U.S.A., 75:7 (1978), 3027–3028.MATHCrossRefMathSciNetGoogle Scholar
  31. [32]
    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.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1980

Authors and Affiliations

  • David S. Tartakoff
    • 1
  1. 1.University of Illinois at Chicago CircleChicagoU.S.A.

Personalised recommendations