The Lavrentiev regularization of the data completion problem

The Lavrentiev regularization method is naturally fitted to the data completion problem, put under the variational form proposed by Ben Belgacem and El Fekih (2005 Inverse Problems 21 1915). We address the important issue of selecting the regularizing parameter. We study an a priori choice and the a posteriori choice by means of the discrepancy principle written on the Kohn?Vogelius function. In both cases, we prove error estimates similar to those expected for Tikhonov's method.