Integral Equations and Operator Theory

, Volume 10, Issue 2, pp 236–257

Boundary integral equations for screen problems in IR3


  • Ernst P. Stephan
    • School of MathematicsGeorgia Institute of Technology

DOI: 10.1007/BF01199079

Cite this article as:
Stephan, E.P. Integr equ oper theory (1987) 10: 236. doi:10.1007/BF01199079


Here we present a new solution procedure for Helmholtz and Laplacian Neumann screen or Dirichlet screen problems in IR3 via boundary integral equations of the first kind having as unknown the jump of the field or of its normal derivative, respectively, across the screen S. Under the assumption of local finite energy we show the equivalence of the integral equations and the original boundary value problems. Via the Wiener-Hopf method in the halfspace, localization and the calculus of pseudodifferential operators we derive existence, uniqueness and regularity results for the solution of our boundary integral equations together with its explicit behavior near the edge of the screen. We give Galerkin schemes based on our integral equations on S and obtain high convergence rates by using special singular elements besides regular splines as test and trial functions.

Copyright information

© Birkhäuser Verlag 1987