Regularization of Ill-Posed Problems with Unbounded Operators

TL;DR

This paper justifies variational regularization and quasisolutions for unbounded, possibly nonlinear operators, providing simple and general theoretical results for solving ill-posed problems.

Contribution

It introduces a straightforward approach to justify regularization methods for unbounded operators, extending the applicability to nonlinear cases.

Findings

Justification of variational regularization for unbounded operators

Extension of quasisolutions method to nonlinear operators

General theoretical results for ill-posed problems with unbounded operators

Abstract

Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.