Tikhonov regularization of nonlinear ill-posed equations under general source condition

Abstract

Tikhonov regularization is one of the widely used procedures for the regularization of nonlinear as well as linear ill-posed problems. The error analysis carried out in most of the works that appeared in last few years on Tikhonov regularization of nonlinear ill-posed problems are under Hölder type source conditions on the unknown solution which is known to be applicable only for mildly ill-posed problems. In this paper we consider Tikhonov regularization of nonlinear ill-posed problems and derive order optimal error estimate under a general source condition together with an a posteriori parameter rule proposed by Scherzer et al., which is applicable for severely ill-posed problems as well.