Two regularization methods for a class of inverse boundary value problems of elliptic type
1 Applied Mathematics Laboratory, University Badji Mokhtar Annaba, P.O. Box 12, Annaba, 23000, Algeria
2 Department of Mathematics, 8 Mai 1945 Guelma University, P.O. Box 401, Guelma, 24000, Algeria
Boundary Value Problems 2013, 2013:178 doi:10.1186/1687-2770-2013-178Published: 2 August 2013
This paper deals with the problem of determining an unknown boundary condition in the boundary value problem , , , with the aid of an extra measurement at an internal point. It is well known that such a problem is severely ill-posed, i.e., the solution does not depend continuously on the data. In order to overcome the instability of the ill-posed problem, we propose two regularization procedures: the first method is based on the spectral truncation, and the second is a version of the Kozlov-Maz’ya iteration method. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution.
MSC: 35R25, 65J20, 35J25.