Inverse Dirichlet to Neumann problem for nodal curves

TL;DR

This paper develops methods for solving inverse boundary value problems on complex nodal curves and applies them to reconstruct the conformal structure of a surface from electrical measurements.

Contribution

It introduces new direct and inverse results for Dirichlet and Neumann problems on nodal curves and provides a novel reconstruction method for surface conformal structures.

Findings

Reconstruction of conformal structure from electrical data

New inverse problem solutions for nodal complex curves

Application to surfaces in Euclidean space

Abstract

This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact surface of the standard three dimensional euclidean space with constant scalar conductivity from electrical current measurements in a neighborhood of one of its points.