Communications in Mathematical Physics

, Volume 340, Issue 2, pp 639–659 | Cite as

Uniqueness in Calderón’s Problem for Conductivities with Unbounded Gradient

  • Boaz HabermanEmail author


We prove uniqueness in the inverse conductivity problem for uniformly elliptic conductivities in \({W^{s,p}(\Omega)}\), where \({\Omega \subset \mathbb{R}^{n}}\) is Lipschitz, \({3\leq n \leq 6}\), and s and p are such that \({ W^{s,p}(\Omega)\not \subset W^{1,\infty}(\Omega)}\). In particular, we obtain uniqueness for conductivities in \({W^{1,n}(\Omega)}\) (n = 3, 4). This improves on the result of the author and Tataru, who assumed that the conductivity is Lipschitz.


Electric Impedance Tomography Fourier Multiplier Cauchy Data Unique Continuation Carleman Estimate 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA

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