The Poisson embedding approach to the Calderón problem

Abstract

We introduce a new approach to the anisotropic Calderón problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calderón type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calderón problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.

arXiv comment48 pages

References in corpus (5)

• Full-wave invisibility of active devices at all frequencies
• Limiting Carleman weights and anisotropic inverse problems
• Sobolev spaces on non-Lipschitz subsets of ${\mathbb{R}}^n$ with application to boundary integral equations on fractal screens
• Full and Partial Cloaking in Electromagnetic Scattering
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Cited by in corpus (4)

• Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
• An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
• Remarks on the anisotropic Calderón problem
• Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds