Reconstruction from boundary measurements for less regular conductivities. (5th October 2016)

• Record Type: Journal Article
• Authors: García, Andoni; Zhang, Guo
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-10-05
• Subjects: inverse conductivity problem -- Dirichlet-to-Neumann map -- Caldern problem -- boundary integral equation -- Bourgain's space; 35R30; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115015
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, following Nachman's idea (1988 Ann. Math. 128 531–76 ) and Haberman and Tataru's idea (2013 Duke Math. J. 162 497–516 ), we reconstruct C 1 conductivity γ or Lipchitz conductivity γ with small enough value of ∣ ∇ log γ ∣ in a Lipschitz domain Ω from the Dirichlet-to-Neumann map Λ γ . In the1 the authors and Brown recover the gradient of a C 1 -conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map Λ γ .