Stable Reconstruction Of Regular 1-Harmonic Maps With A Given Trace At The Boundary

Keywords

1-Laplacian; boundary value problems; characteristics; current density impedance imaging; global convergence

Abstract

We consider the numerical solvability of the Dirichlet problem for the 1-Laplacian in a planar domain endowed with a metric conformal with the Euclidean one. Provided that a regular solution exists, we present a globally convergent method to find it. The global convergence allows to show a local stability in the Dirichlet problem for the 1-Laplacian nearby regular solutions. Such problems occur in conductivity imaging, when knowledge of the magnitude of the current density field (generated by an imposed boundary voltage) is available inside. Numerical experiments illustrate the feasibility of the convergent algorithm in the context of the conductivity imaging problem.

Publication Date

6-3-2015

Publication Title

Applicable Analysis

Volume

94

Issue

6

Number of Pages

1098-1115

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/00036811.2014.918260

Socpus ID

84925794182 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84925794182

This document is currently not available here.

Share

COinS