Reconstructions from boundary measurements on admissible manifolds

Details Reconstructions from boundary measurements on admissible manifolds Reconstructions from boundary measurements on admissible manifolds

2010-11-02

arxiv.org/abs/1011.0749v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $\Delta_g$. This is a constructive version of earlier uniqueness results by Dos Santos Ferreira et al. on admissible manifolds, and extends the reconstruction procedure of Nachman in Euclidean space. The main points are the derivation of a boundary integral equation characterizing the boundary values of complex geometrical optics solutions, and the development of associated layer potentials adapted to a cylindrical geometry.

Affiliated with

Also associated with

No associations

Rating

Reconstructions from boundary measurements on admissible manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reconstructions from boundary measurements on admissible manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reconstructions from boundary measurements on admissible manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601787