Author(s)

Q. Wangi & K. Onishi

Abstract

The Laplace equation in a bounded domain of two dimensions is considered, subjected to data generally prescribed on the boundary. Problems consist of under-determined boundary value problem, conventional boundary value problem, Cauchy problem, and over-determined boundary value problem. The purpose of the paper is to present a unified new treatment of those problems in order to provide a numerical modelling of groundwater and aquifer. 1 Introduction Let Q C P? be a domain bounded by a smooth curve F with the Cartesian coordinates x = (#i,£2)- We consider the Laplace equation -Au(x) = 0 in ft. (1) Let n denote the outward unit

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