Uniqueness of minimizers of weighted least gradient problems arising in conductivity imaging

Abstract

We prove uniqueness for minimizers of the weighted least gradient problem \[\inf \left\lbrace \int_Ω a|Du|: \ \ u\in BV(Ω), \ \ u|_{\partial Ω}=f \right\rbrace.\] The weight function $a$ is assumed to be continuous and it is allowed to vanish in certain subsets of $\Omega$. Existence is assumed a priori. Our approach is motivated by the hybrid inverse problem of imaging electric conductivity from interior knowledge (obtainable by MRI) of the magnitude of one current density vector field.

Cited by in corpus (1)

• Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class