An inverse anisotropic conductivity problem induced bytwisting a homogeneous cylindrical domain

Abstract

We consider the inverse problem of determining the unknown function $\alpha :\mathbb{R}\to \mathbb{R}$ from the DN map associated to the operator $\mbox{div}(A(x',α(x\_3))\nabla \cdot)$ acting in the infinite straight cylindrical waveguide $\Omega =\omega \times \mathbb{R}$, where $\omega$ is a bounded domain of ${\mathbb{R}}^2$. Here $A=(A\_ij(x))$, $x=(x^{\prime },x\_3)\in \Omega$, is a matrix-valued metric on $\Omega$ obtained by straightening a twisted waveguide. This inverse anisotropic conductivity problem remains generally open, unless the unknown function $\alpha$ is assumed to be constant. In this case we prove Lipschitz stability in the determination of $\alpha$ from the corresponding DN map. The same result remains valid upon substituting a suitable approximation of the DN map, provided the function $\alpha$ is sufficiently close to some {\it a priori} fixed constant.

References in corpus (1)

• Stable Determination of Time-Dependent Scalar Potential From Boundary Measurements in a Periodic Quantum Waveguide

Cited by in corpus (4)

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• Stable Determination of Time-Dependent Scalar Potential From Boundary Measurements in a Periodic Quantum Waveguide
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• Stability estimate for the aligned magnetic field in a periodic quantum waveguide from dirichlet-to-neumann map