We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide. © 2011 Elsevier Masson SAS.
Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
SANTACESARIA, MATTEO
2011-01-01
Abstract
We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation -δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide. © 2011 Elsevier Masson SAS.File in questo prodotto:
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