Skip to main content
SpringerLink
Log in

Estimates for Green's matrices of elliptic systems byL p theory

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Summary

We prove existence and optimal decay properties of a Green's matrix for elliptic systems of second order. The results follow from regularity theorems in weak Lebesgue spaces which can be obtained from the classicalL p theory using interpolation theorems.

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

Similar content being viewed by others

References

  1. Butzer, P.L. and Berens, H.: Semi-Groups of Operators and Approximation, Springer, 1967

  2. Fuchs, M.: The Green Matrix for Elliptic Systems which satisfy the Legendre-Hadamard Condition, Manuscr. math.46, 97–115 (1984)

    Article  Google Scholar 

  3. Fuchs, M.: The Green Matrix for Strongly Elliptic Systems of Second Order with Continuous Coefficients, Zeitschrift Analysis Anwend.5, 507–531 (1986)

    Google Scholar 

  4. Grüter, M. and Widman, K. O.: The Green Function for Uniformly Elliptic Equations, Manuscr. math.37, 303–342 (1982)

    Article  Google Scholar 

  5. L. Hörmander, L.: Linear Partial Differential Operators, Springer, 1976

  6. Hildebrandt, S. and Widman, K. O.: Some Regularity Results for Quasilinear Elliptic Systems of Second Order, Math. Z.142, 67–86 (1975)

    Article  MathSciNet  Google Scholar 

  7. Hildebrandt, S. and Widman, K. O.: On the Hölder Continuity of Weak Solutions of Quasilinear Elliptic Systems of Second Order, Ann. Scuola Norm. Sup. Pisa (IV)4, 145–178 (1977)

    MathSciNet  Google Scholar 

  8. John, F.: Plane Waves and Spherical Means, Springer, 1955

  9. Kufner, A., John, O. and Fučík, S.: Function Spaces, Noordhoff International Publishing, Leyden, 1977

    MATH  Google Scholar 

  10. Littman, W., Stampacchia, G. and Weinberger, H. F.: Regular Points for Elliptic Equations with Discontinuous Coefficients, Ann. Scuola Norm. Sup. Pisa (III)17, 43–77 (1963)

    MathSciNet  Google Scholar 

  11. Morrey, C.B.: Multiple Integrals in the Calculus of Variations, Springer, 1966

  12. Steinhauer, M.: Funktionenräume vom Campanato-Typ und Regularitätseigenschaften elliptischer Systeme zweiter Ordnung, Diplomarbeit, Bonn, (1993)

  13. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970

    MATH  Google Scholar 

  14. Stein, E.M. and Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1971

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität Freiburg, Albertstr. 23b, 79104, Freiburg, Germany

    G. Dolzmann & S. Müller

Authors
  1. G. Dolzmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dolzmann, G., Müller, S. Estimates for Green's matrices of elliptic systems byL p theory. Manuscripta Math 88, 261–273 (1995). https://doi.org/10.1007/BF02567822

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567822

Key words

Search

Navigation