Recovering a quasilinear conductivity from boundary measurements. (24th December 2020)

• Record Type: Journal Article
• Authors: Shankar, Ravi
• Is Part Of: Inverse problems. Volume 37:Number 1(2021)
• Publication Date: 2020-12-24
• Subjects: Calderon problem -- elliptic -- nonlinear -- quasilinear -- Dirichlet-to-Neumann map -- conductivity -- linearization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abced7
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the Calderón type inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result of Muñoz and Uhlmann to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.