Identification of a Singular Point Using Dirichlet-Neumann Data for a Harmonic Function

Abstract

An idea is presented about a possible numerical identification method for the location of an isolated essential singular point of the harmonic function in the plane. The method is based on the boundary element solution to the Cauchy problem of the Laplace equation, in which Dirichlet and Neumann data are measured on arbitrary parts of the boundary to some extent. Discussion is concerned with only one sample problem whose numerical solutions exhibit oscillating odd behavior near the singular point. The solutions are scanned on family of lines in two independent directions.