On the stable recovery of a metric from the hyperbolic DN map with incomplete data

Plamen  Stefanov; Gunther  Uhlmann; Andras  Vasy

doi:10.3934/ipi.2016035

Article Contents

2016, Volume 10, Issue 4: 1141-1147. Doi: 10.3934/ipi.2016035

This issue Previous Article Location of eigenvalues for the wave equation with dissipative boundary conditions Next Article A minimal surface criterion for graph partitioning

On the stable recovery of a metric from the hyperbolic DN map with incomplete data

1.
Department of Mathematics, Purdue University, West Lafayette, IN 47907
2.
Department of Mathematics, University of Washington, Seattle, WA 9819A
3.
Department of Mathematics, Stanford University, Stanford, CA 94305

Received: May 2015

Revised: July 2016

Published: November 2016

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Abstract

We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a consequence, we prove uniqueness of recovery a conformal factor (sound speed) locally under some conditions on the latter.

Keywords:

Inverse problem,
DN map,
metric.

Mathematics Subject Classification: Primary: 35R30.

Citation:

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