Stability of the Calderón problem in admissible geometries

Pedro Caro; Mikko Salo

doi:10.3934/ipi.2014.8.939

Article Contents

2014, Volume 8, Issue 4: 939-957. Doi: 10.3934/ipi.2014.8.939

This issue Previous Article Foreword Next Article Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem

Stability of the Calderón problem in admissible geometries

Pedro Caro^1, and
Mikko Salo^2,

1.
Instituto de Ciencias Matemáticas - CSIC, Nicolás Cabrera 13-15, Campus de Cantoblanco UAM, 28049 Madrid
2.
Department of Mathematics and Statistics, University of Helsinki and University of Jyväskylä, P.O. Box 35 FI-40014 Jyväskylä

Received: April 30, 2014

Revised: August 31, 2014

Published: October 2014

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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.

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Mathematics Subject Classification: Primary: 35R30, 58J32; Secondary: 35J10, 35R01.

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