Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem

Fuente: arXiv
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Main Authors: Garde, Henrik, Johansson, David, Zacharopoulos, Thanasis
Format: Preprint
Published: 2026
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author Garde, Henrik
Johansson, David
Zacharopoulos, Thanasis
author_facet Garde, Henrik
Johansson, David
Zacharopoulos, Thanasis
contents We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calderón problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the anisotropic real conductivity and the anisotropic permittivity, and the results hold in any spatial dimension $d \geq 2$. We assume that the inclusion boundaries can be reached from the domain boundary via a set on which the background conductivity is self-adjoint, and that a definiteness condition holds near the inclusion boundaries. Away from the inclusion boundaries we allow general $L^\infty$ non-self-adjoint perturbations. We only require unique continuation based on the self-adjoint part of the background conductivity, thus making the methods compatible with generic unique continuation results.
format Preprint
id arxiv_https___arxiv_org_abs_2605_05021
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem
Garde, Henrik
Johansson, David
Zacharopoulos, Thanasis
Analysis of PDEs
35R30, 35R05, 47H05
We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calderón problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the anisotropic real conductivity and the anisotropic permittivity, and the results hold in any spatial dimension $d \geq 2$. We assume that the inclusion boundaries can be reached from the domain boundary via a set on which the background conductivity is self-adjoint, and that a definiteness condition holds near the inclusion boundaries. Away from the inclusion boundaries we allow general $L^\infty$ non-self-adjoint perturbations. We only require unique continuation based on the self-adjoint part of the background conductivity, thus making the methods compatible with generic unique continuation results.
title Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem
topic Analysis of PDEs
35R30, 35R05, 47H05
url https://arxiv.org/abs/2605.05021