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Well-posedness of Helmholtz and Laplace Problems in Unbounded Domains with Multiple Screens

by C. Jerez-Hanckes and J. Pinto

(Report number 2018-45)

Abstract
We present proofs for the existence and uniqueness of solutions of Helmholtz and Laplace problems in unbounded domains with either Dirichlet or Neumann boundary conditions on finite collections of open arcs (in 2D) or screens (3D). This extends existent results for a single arc/screen and provides a constructive solution strategy based on boundary integral operators that is shown to apply to more general second order coercive equations.

Keywords: Laplace equation, Helmholtz equation, boundary integral equations, screen problems, crack problems

@Techreport{JP18_799,
  author = {C. Jerez-Hanckes and J. Pinto},
  title = {Well-posedness of Helmholtz and Laplace Problems in Unbounded Domains with Multiple Screens},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2018-45},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2018/2018-45.pdf },
  year = {2018}
}

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