Reduction an Inverse Problem to a System of Second Kind Fredholm Integral Equations with No Singularities

Abstract

In this article, we deal with an inverse problem concerning the two-dimensional Laplace equation with local boundary conditions on a bounded region. In this problem, the goal is to reduce it into a system of Fredholm integral equations of the second kind involving kernels with weakly/or no singularities (Fredholm property) by considering some additional conditions on the parameters of the problem. Finally, the method is carried out on an example, to show the simplicity and efficiency of the method.