Inverse Problems and Imaging (IPI)

Stability of the Calderón problem in admissible geometries

Pages: 939 - 957, Volume 8, Issue 4, November 2014      doi:10.3934/ipi.2014.8.939

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Pedro Caro - Instituto de Ciencias Matemáticas - CSIC, Nicolás Cabrera 13-15, Campus de Cantoblanco UAM, 28049 Madrid, Spain (email)
Mikko Salo - Department of Mathematics and Statistics, University of Helsinki and University of Jyväskylä, P.O. Box 35 FI-40014 Jyväskylä, Finland (email)

Abstract: In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to the uniqueness results in [13]. These inverse problems arise naturally when studying the anisotropic Calderón problem.

Keywords:  Inverse boundary value problems, Calderón problem, stability.
Mathematics Subject Classification:  Primary: 35R30, 58J32; Secondary: 35J10, 35R01.

Received: May 2014;      Revised: September 2014;      Available Online: November 2014.