Ann-dimensional Borg-Levinson theorem

The Calderón problem for conormal potentials I: Global uniqueness and reconstruction

“…Global uniqueness was established in [32] for n ≥ 3 (for smooth potentials) and [26] for n = 2; for n ≥ 3 this was extended to q ∈ L ∞ in [27]. The regularity was further lowered to q ∈ L n 2 in unpublished work of R. Lavine and A. Nachman and to potentials of small norm in the Fefferman-Phong class in [4].…”

Direct Reconstructions of Conductivities from Boundary Measurements

“…In [72] Sylvester and Uhlmann showed that if ∂Ω is C ∞ , then Λ γ uniquely determines γ ∈ C ∞ (Ω) in dimensions n ≥ 3. Their smoothness assumption on γ was relaxed to γ ∈ W 2,∞ (Ω) in [54], and ∂Ω ∈ C 1,1 in [51], and ∂Ω Lipschitz in [4]. A logarithmic continuous dependence result of γ on Λ γ is given in [3].…”

Calderón’s inverse conductivity problem in the plane

“…[23], [24]) but the original problem of Calderón has still remained unsolved. In dimensions three and higher the uniqueness is known for conductivities in W 3/2,∞ (Ω), see [26], and in two dimensions the best result so far was σ ∈ W 1,p (Ω), p > 2, [10].…”