Stability Estimates for Solution of Neumann-Type Overdetermined Elliptic Problem

Abstract

This paper addresses estimation of the solution of inverse problem for the elliptic type equation with second kind boundary conditions and Neumann-type overdetermination at the interior point. We prove various estimates for the solution of this identification problem. Then, the first order accuracy stable difference scheme is studied. The stability, almost coercive stability, and coercive stability inequalities for its solution are obtained. The theoretical results can be applied to investigate identification problems for multidimensional elliptic equation with different kind of boundary conditions.