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Uniqueness in Calderón’s problem with Lipschitz conductivities. (English) Zbl 1260.35251

Summary: We use \(X^{s,b}\)-inspired spaces to prove a uniqueness result for Calderón’s problem in a Lipschitz domain \(\Omega\) under the assumption that the conductivity lies in the space \(W^{1,\infty}(\overline{\Omega})\). 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.

MSC:

35R30 Inverse problems for PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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References:

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