Comments on the determination of the conductivity at the boundary from the Dirichlet-to-Neumann map

TL;DR

This paper revisits the stability of boundary conductivity determination from the Dirichlet-to-Neumann map, clarifying existing proofs and discussing implications without presenting new primary results.

Contribution

It clarifies and comments on existing methods for boundary conductivity determination, providing insights and consequences of stability inequalities.

Findings

Clarification of proof techniques for boundary conductivity determination.

Discussion of implications of stability inequalities.

Comparison of singular and localized oscillating solutions methods.

Abstract

We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions. Our primary objective is not establishing new results on this subject even if the present work contains some new ones. We mainly clarify some points in the existing proofs and make some comments. We also derive some consequences of the stability inequality of the determination of the conductivity at the boundary from the Dirichlet-to-Neumann map.