Determining an anisotropic conductivity by boundary measurements: stability at the boundary

2023/03/30 by Alessandrini, Giovanni, Gaburro, Romina, Sincich, Eva
#86A22 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35R30 #Secondary: 35J25

paper · doi:10.48550/arxiv.2303.17362

Abstract

We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body by means of the so called local Neumann to Dirichlet map on a curved portion Σ of the boundary. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in \citeAl-dH-G, we provide a Hölder stability estimate on Σ when the conductivity is a priori known to be a constant matrix near Σ.

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