Author(s)

Yu. A. Melnikov & J.O. Powell

Abstract

A cavity, or a flux on the boundary of a cavity inside of a planar domain is to be determined from electrostatic or thermostatic measurements taken on the domain boundary. This inverse problem is solved by an optimization method, along with the Green's function modification of a boundary integral formulation of an elliptic partial differential equation which models voltage or heat conduc- tion inside of the domain. 1 Introduction Melnikov^ has developed techniques which make it possible to obtain rep- resentations for Green's functions or matrices for elliptic partial differential equations with mixed boundary conditions, on domains of a variety of sim- ple shapes. These Green's functions have found application

Keywords