RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA

By A. Bukhgeǐm, Gunther Uhlmann. 2002

265 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d65dc7c985f95d0fb7f124bf1c09febc0307d865

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computer Vision and Pattern Recognition

In Mathematical Physics

Citations in the corpus

Calderon inverse Problem with partial data on Riemann Surfaces (2009, methodology): “ 0,u= 0 in ∂Ω \Γ1} determine the domain Ω, the metric, the potential? For a ﬁxed domain of Rn, the recovery of the potential if n>2 with partial data measurements was initiated by Bukhgeim-Uhlmann [7] and later improved by Kenig-Sjo¨strand-Uhlmann [18] to the case where Γ1 and Γ2 are respectively”
The Calderón Problem with Partial Data for Less Smooth Conductivities (2006, methodology): “2) to the case of partial data (even though we require slightly more smoothness here) and a generalization of Bukhgeim and Uhlmann (2002, Corollary 0.2) to the case of less regular conductivities (note, however, that in Bukhgeim and Uhlmann, 2002, Corollary 0.2, no assumption on the normal derivativ”
The Calderón problem with partial data in two dimensions (2010, background): “In dimensions n ≥ 3, [8] proves global uniqueness in determining a bounded potential for the Schrödinger equation with Dirichlet data supported on the whole boundary and Neumann data measured in roughly half the boundary.”
The Calderón problem with partial data (2004, unknown): “Mathematics Subject Classification 2000: 35R30”
Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map (2008, unknown): “Then for each ω ∈ Vε(ω0) Σ−, ε2 (ω) ⊂ Σ−,ε(ω0).”
Partial Cauchy data for general second order elliptic operators in two dimensions (2010, methodology): “The case of partial data was considered in [10], based on the methods of [15] and [6], with an improvement on the regularity of the coefficients in [16].”
Inverse problems: seeing the unseen (2014, methodology): “Stability estimates for the magnetic Schrödinger operator with partial data in the setting of [35] can be found in [198].”
Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term (2016, methodology): “n and dynamical Schrödinger equations [3, 16, 18, 24, 33, 34, 35]. We point out that, concerning the elliptic case, a stability estimate corresponding to the uniqueness result by Bukhgeim and Uhlmann [6] was established by Heck and Wang [27]. This result was improved by the authors and Soccorsi in [”
On uniqueness in the inverse conductivity problem with local data (2007, methodology): “We add new ingredients to the SylvesterUhlmann method.”