Global counterexamples to uniqueness  for a Calder\'on problem with smooth conductivities.

Abstract: Let $\Omega \subset \R^n$, $n \geq 3$, be a fixed smooth bounded domain, and let $\gamma$ be a smooth conductivity in $\overline{\Omega}$. Consider a non-zero frequency $\lambda_0$ which does not belong to the Dirichlet spectrum of $L_\gamma = -{\rm div} (\gamma \nabla \cdot)$. Then, there exists an infinite number of pairs of smooth non-isometric conductivities $(\gamma_1, \gamma_2)$ on $\overline{\Omega}$, which are close to $\gamma$ and such that the associated DN maps at frequency $\lambda_0$ are identical.

This is a joint work with Thierry Daudé, Bernard Helffer and Niky Kamran.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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