Skip to main content
SpringerLink
Log in

Remarks on the reflection principle for harmonic functions

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

  • [ACL] N. Aronszajn, Th. Creese and L. Lipkin,Polyharmonic Functions, Clarendon Press, Oxford, 1983.

    MATH  Google Scholar 

  • [Av] V. Avanissian,Cellule d'Harmonicité et Prolongement Analytique Complexe, Hermann, Paris, 1985.

    MATH  Google Scholar 

  • [CH] R. Courant and D. Hilbert,Methods of Mathematical Physics, Vol. II, Interscience, New York, 1962.

    MATH  Google Scholar 

  • [Da] P. Davis,The Schwarz Function and its Applications, Carus Mathematical Monographs No. 17, MAA, 1979.

  • [De] K. Deimling,Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.

    MATH  Google Scholar 

  • [DNF] B. A. Dubrovin, S. P. Novikov and A. T. Fomenko,Modern Geometry, Vol. I, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  • [Ga] P. Garabedian,Partial differential equations with more than two independent variables in the complex domain, J. Math. Mech.9 (1960), 241–271.

    MATH  MathSciNet  Google Scholar 

  • [GS] I. M. Gelfand and G. E. Shilov,Generalized Functions, Vol. II, Academic Press, New York, 1968 (translated from Russian).

    Google Scholar 

  • [He] P. Henrici,A survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficients, Z. Angew. Math. Phys.8 (1957), 169–203.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ke] O. Kellogg,Foundations of Potential Theory, Ungar, New York, 1929.

    Google Scholar 

  • [He] H. Lewy,On the reflection laws of second order differential equations in two independent variables, Bull. Am. Math. Soc.65 (1959), 37–58.

    MATH  MathSciNet  Google Scholar 

  • [Mo] C. B. Morrey,On the analyticity of the solutions of analytic non-linear elliptic systems of partial differential equations, I and II, Am. J. Math.80 (1958), 198–237.

    Article  MathSciNet  Google Scholar 

  • [Ni] L. Nirenberg,On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, (3)13 (1959), 115–162.

    MathSciNet  Google Scholar 

  • [PW] M. Protter and H. Weinberger,Maximum Principles in Differential Equations, Springer-Verlag, Berlin, 1984.

    MATH  Google Scholar 

  • [St] E. Study,Einige elementare Bemerkungen über den Prozess der analytischen Fortsetzung, Math. Ann.63 (1907), 239–245.

    Article  MathSciNet  Google Scholar 

  • [Ve] I. N. Vekua,New Methods for Solving Elliptic Equations, North-Holland Publ. Co., Amsterdam, 1967 (translated from Russian).

    MATH  Google Scholar 

  • [WW] E. T. Whittaker and G. N. Watson,A Course of Modern Analysis, 4th ed., Cambridge University Press, 1958.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Arkansas, 72701, Fayetteville, AR, USA

    Dmitry Khavinson

  2. Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Harold S. Shapiro

Authors
  1. Dmitry Khavinson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harold S. Shapiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author was partially supported by the National Science Foundation under grant DMS-8618755.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khavinson, D., Shapiro, H.S. Remarks on the reflection principle for harmonic functions. J. Anal. Math. 54, 60–76 (1990). https://doi.org/10.1007/BF02796142

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02796142

Keywords

Search

Navigation