Skip to main content
SpringerLink
Log in

On strongly elliptic singular integral operators with piecewise continuous coefficients

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

The concept of strongly elliptic operators is one of the main tools for approximating the solution of boundary integral equations by finite element methods (see [4-10]). In the present paper necessary and sufficient conditions for the strong ellipticity of singular integral operators with piecewise continuous matrix coefficients on a closed or open Ljapunov curve are obtained.

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. Gohberg, I.C. and Krupnik, N.Ya.: Algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients. Funct. Anal. and its Applic.4 (1970), 193–201.

    Google Scholar 

  2. Gohberg, I.C. and Krupnik, N.Ya.: On symbols of one-dimensional singular integral operators on an open curve. Dokl. Akad. Nauk USSR,191, 1 (1970), 12–15 (Russian).

    Google Scholar 

  3. Prößdorf, S.: Starke Elliptizität singulärer Integral-operatoren und Spline-Approximation. In: Linear and Complex Analysis Problem Book — 199 Research Problems (V.P. Havin, S.V. Hruščëv and N.K. Nikol'ski eds.). Lecture Notes in Math. 1043, Springer Verlag Berlin Heidelberg, 1984.

    Google Scholar 

  4. Prößdorf, S. and Rathsfeld, A.: A spline collocation method for singular integral equations with piecewise continuous coefficients. Integral Equations and Operator Theory, Vol. 7 (1984), 536–560.

    Google Scholar 

  5. Prößdorf, S. and Rathsfeld, A.: On spline Galerkin methos for singular integral equations with piecewise continuous coefficients, in preparation.

  6. Prößdorf, S. and Schmidt, G.: A finite element collocation method for singular integral equations. Math. Nachr.100 (1981), 33–60.

    Google Scholar 

  7. Prößdorf, S. and Schmidt, G.: A finite element collocation method for systems of singular integral equations. Preprint P-MATH-26/81, Berlin 1981.

  8. Schmidt, G.: On spline collocation methods for boundary integral equations in the plane. Math. Methods in the Appl. Sciences 7, to appear.

  9. Schmidt, G.: On ɛ-collocation for pseudodifferential equations on a closed curve. Math. Nachr., in print.

  10. Wendland, W.L.: On Galerkin collocation methods for integral equations of elliptic boundary value problems. Intern. Series Num. Math.53 (1980), Birkhäuser-Basel, 244–275.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Akademie der Wissenschaften der DDR, Mohrenstraße 39, DDR-1080, Berlin

    Siegfried Prößdorf & Andreas Rathsfeld

Authors
  1. Siegfried Prößdorf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Rathsfeld
    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

Prößdorf, S., Rathsfeld, A. On strongly elliptic singular integral operators with piecewise continuous coefficients. Integr equ oper theory 8, 825–841 (1985). https://doi.org/10.1007/BF01213793

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01213793

Keywords

Search

Navigation