Limiting Carleman weights and anisotropic inverse problems
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Cites background from "Limiting Carleman weights and aniso..."
...The latter fact follows from the unique boundary determination of potentials from the Dirichlet-to-Neumann map (see for instance [12], [29])....
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Cites background or methods from "Limiting Carleman weights and aniso..."
...In [52] we have classified locally all the LCW in Euclidean space....
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...Below we give a characterization of all the LCW in Rn , n > 2, see [52]....
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...We review below the progress that has been made on this problem based on [52]....
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...We review the recent construction of complex geometrical optics construction for a class of Riemannian manifolds based on [52]....
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References
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"Limiting Carleman weights and aniso..." refers background in this paper
...We denote by p ∼ ∑ pj the asymptotic sym of symbols, see [10] for these basic facts....
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"Limiting Carleman weights and aniso..." refers background in this paper
...In dimensions n ≥ 3 this was known earlier for metrics conformal to the Euclidean metric [32], conformal to the hyperbolic metric [11], and analytic metrics in the same conformal class [19] (based on [18])....
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...These results are based on special complex geometrical optics solutions to elliptic equations, introduced in [32]....
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...This result was known previously in dimensions n ≥ 3 for the Euclidean metric [32] and for the hyperbolic metric [11]....
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