Uniqueness in Calderón’s problem with Lipschitz conductivities
By Boaz Haberman, D. Tataru. 2011
160 citations recorded by the source corpus.
We use X^{s,b}-inspired spaces to prove a uniqueness result for Calderon's problem in a Lipschitz domain under the assumption that the conductivity is Lipschitz. For Lipschitz conductivities, we obtain uniqueness for conductivities close to the identity in a suitable sense. We also prove uniqueness for arbitrary C^1 conductivities.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6e93223825ce087a47bdb8e57a6d8af7aaeb8f2
How researchers see this paper
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In Computational Theory and Mathematics
- Katya Krupchyk
- Gunther Uhlmann
- Mikko Salo
- Ali Feizmohammadi
- Yavar Kian
- C. Carstea
- Keith McKenzie Rogers
- Valter Pohjola
In Control and Systems Engineering
In Mathematical Physics
- Katya Krupchyk
- Gunther Uhlmann
- Mikko Salo
- Ali Feizmohammadi
- Yavar Kian
- C. Carstea
- Bastian von Harrach
- Keith McKenzie Rogers
Citations in the corpus
- GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES (2014, methodology): “These spaces, first considered by Haberman and Tataru, are adapted to the structure of the equation in the spirit of Bourgain spaces.”
- The Calderón inverse problem for isotropic quasilinear conductivities (2021, result): “This includes results in dimension two [3, 39], results with less regular conductivities [1, 17], results with measurements restricted to some portion of the boundary [4, 21, 25] and results in the setting of Riemannian manifolds [12, 16, 34, 28].”
- Monotonicity and local uniqueness for the Helmholtz equation (2017, background): “For a short list of seminal contributions for full boundary data let us refer to [Kohn and Vogelius 1984; 1985; Druskin 1998; Sylvester and Uhlmann 1987; Nachman 1996; Astala and Päivärinta 2006; Haberman and Tataru 2013; Caro and Rogers 2016].”
- Inverse problems: seeing the unseen (2014, background): “Recently Haberman and Tataru in a very nice article [75] have extended the uniqueness result to C1 conductivities or small in the W 1,∞ norm.”