Recovering a potential from Cauchy data in the two-dimensional case

By A. Bukhgeǐm. 2008

293 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/79439314e4058a38593224d4360511a75c234999

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In Applied Mathematics

In Geophysics

In Mathematical Physics

Citations in the corpus

Limiting Carleman weights and anisotropic inverse problems (2008, background): “We remark that in the two dimensional case global uniqueness for the Euclidean metric was proved only recently [ 6 ] (earlier results considered potentials coming from conductivities [24] or a generic class of potentials [32]).”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “For recent development on new kinds of cgo solutions for inverse problems, see [ 16 , 20, 47, 55].”
The Calderón problem with partial data in two dimensions (2010, background): “recent breakthrough result of Bukhgeim [ 7 ] gives unique identifiability of the potential from Cauchy data measured on the whole boundary for the associated Schr¨odinger equation.”
Calderon inverse Problem with partial data on Riemann Surfaces (2009, background): “…D : C∞(M0, E) → C∞(M0, T ∗0,1 ⊗ E) be a Cauchy-Riemann operator with smooth coefficients on M0, acting on sections of the bundle E. Observe that in the case when E = M0 × C is the trivial line bundle with the natural complex structure on M0, then D can be taken as the operator ∂ introduced in (2).”
Identification of a Connection from Cauchy Data on a Riemann Surface with Boundary (2010, methodology): “We do not give details since it is essentially the same idea as [3], but essentially the method is to compare to case V1 = V to the free case V2 = 0 and use complex geometric optic (or Faddeev type) solutions F 1 h , F 2 h for h → 0, together with the Green formula as we did above for identification”
The Calderón problem for variable coefficients nonlocal elliptic operators (2017, background): “Later on the same result has been proved in dimension n = 2 also in [5].”