Numerische Mathematik

, Volume 58, Issue 1, pp 465–478 | Cite as

Lp estimates of boundary integral equations for some nonlinear boundary value problems

  • P. P. B. Eggermont
  • J. Saranen
Article

Summary

Recently, Galerkin and collocation methods have been analyzed for boundary integral equation formulations of some potential problems in the plane with nonlinear boundary conditions, and stability results and error estimates in theH1/2-norm have been proved (Ruotsalainen and Wendland, and Ruotsalainen and Saranen). We show that these results extend toLp setting without any extra conditions. These extensions are proved by studying the uniform boundedness of the inverses of the linearized integral operators, and then considering the nonlinear equations. The fact that inH1/2 setting the nonlinear operator is a homeomorphism with Lipschitz continuous inverse plays a crucial role. Optimal error estimates for the Galerkin and collocation method inLp space then follow.

Subject classification

65R20 65N20 45L10 47A10 CR: G1.9 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • P. P. B. Eggermont
    • 1
    • 2
  • J. Saranen
    • 1
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Faculty of Technology, Section of MathematicsUniversity of OuluOuluFinland

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