Effectivized Holder-logarithmic stability estimates for the Gel'fand inverse problem

Mikhail Isaev (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in $L^2$ and $L^\infty$ norms for the coefficient difference and related stability efficiently increases with increasing energy and/or coefficient difference regularity. Comparisons with preceeding results are given.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Mikhail Isaev, Roman Novikov. Effectivized Holder-logarithmic stability estimates for the Gel'fand inverse problem. Inverse Problems, 2014, 30 (9), pp.19. ⟨hal-00968926⟩