Uniqueness Of Minimizers Of Weighted Least Gradient Problems Arising In Hybrid Inverse Problems

Keywords

31A25; 35J60; 35R30; 62P10

Abstract

We study the question of uniqueness of minimizers of the weighted least gradient problem min{∫Ω|Dv|a:v∈BVloc(Ω\S),v|∂Ω=f},where ∫ Ω| Dv| a is the total variation with respect to the weight function a and S is the set of zeros of the function a. In contrast with previous results, which assume that the weight a∈ C1 , 1(Ω) and is bounded away from zero, here a is only assumed to be continuous, and is allowed to vanish and also be discontinuous in certain subsets of Ω. We assume instead existence of a C1 minimizer. This problem arises naturally in the hybrid inverse problem of imaging electric conductivity from interior knowledge of the magnitude of one current density vector field, where existence of a C1 minimizer is known a priori.

Publication Date

2-1-2018

Publication Title

Calculus of Variations and Partial Differential Equations

Volume

57

Issue

1

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00526-017-1274-x

Socpus ID

85037353736 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85037353736

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