On the Regularization Method for Solving Ill-Posed Problems with Linear Closed Densely Operators - Kinh, Nguyen Van (Transactions on Engineering and Computing Sciences, 2023)
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.