Stable reconstruction of regular 1-Harmonic maps with a given trace at the boundary

    Authors

    A. Tamasan; A. Timonov;J. Veras

    Comments

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    Abbreviated Journal Title

    Appl. Anal.

    Keywords

    35R30; 31A25; 35J60; characteristics; boundary value problems; global; convergence; 1-Laplacian; current density impedance imaging; PARTIAL-DIFFERENTIAL-EQUATIONS; MAGNETIC-RESONANCE; CURRENT-DENSITY; Mathematics, Applied

    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.

    Journal Title

    Applicable Analysis

    Volume

    94

    Issue/Number

    6

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    1098

    Last Page

    1115

    WOS Identifier

    WOS:000351774000002

    ISSN

    0003-6811

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