An inverse anisotropic conductivity problem induced bytwisting a homogeneous cylindrical domain

We consider the inverse problem of determining the unknown function $\alpha: $\mathbb{R}$ \rightarrow $\mathbb{R}$$fromtheDNmapassociatedtotheoperator$\mbox{div}(A(x’,\alpha (x_3))\nabla \cdot)$ acting in the infinite straight cylindrical waveguide $\mathrm{\Omega }=\omega \times \mathbb{R}$, where $\omega$ is a bounded domain of ${\mathbb{R}}^2$. Here $A=(A\mathrm{\_}ij(x))$, $x=(x’,x_3) \in \Omega$,isamatrix-valuedmetricon$\Omega$ 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.