Reconstruction for the Calderón problem with Lipschitz conductivities

2024/01/11 by Pedro Caro, Caro, Pedro, María Ángeles García‐Ferrero +3 · 1 citation
Mathematics · Computer Science · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2401.06120

Abstract

We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz continuous. To determine the conductivity we first solve an associated integral equation locally, finding solutions in H¹(B), where B is a ball that properly contains the body. A key ingredient is to equip this Sobolev space with an equivalent norm which depends on two auxiliary parameters that can be chosen to yield a contraction.

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