On the Regularization Method for Solving Ill-Posed Problems with Linear Closed Densely Operators

Abstract

Let  be a linear, closed, densely defined unbounded operator, where  and  are Hilbert spaces. Assume that  is not boundedly invertible. If equation (1)  is solvable, and if    then the following results are provided: Problem has a unique global minimizer  for any , and . There is a function α(δ),  such that , where  is the unique minimal-norm solution to (1). In this paper we introduce the regularization method solving equation (1) with  being a linear, closed, densely defined unbounded oprator. At the same time give an application to the weak derivative operator equation.