The solution of a mixed boundary value problem for the Laplace equation in a multiply connected domain

Abstract

Here we apply the Cauchy integral method for the Laplace equation in multiply connected domains when the data on each boundary component has the form of the Dirichlet condition or the form of the Neumann condition. This analytic method gives highly accurate results. We give examples of applications of the method.

Keywords

• Cauchy integral
• Laplace equation
• mixed boundary value problem
• multiply connected domain
• approximate solution