79 citations · 82 across the 8 of their papers we have counts for
9 papers
Inverse Problems for the Monge-Ampère Equation: Linearization and Nonlinear Recovery
Gunther Uhlmann, Philipp Zimmermann
We study inverse boundary value problems for the fully nonlinear Monge-Ampère equation in a bounded domain. Motivated by Calderón-type problems, we in…
A nonlocal-to-local transfer principle for parabolic Calderón problems
Ching-Lung Lin, Yi-Hsuan Lin, Gunther Uhlmann
We prove a nonlocal-to-local transfer principle for fractional powers of variable coefficient parabolic operators. Let , where is a uniformly…
A Reduction of the Fractional Calderón Problem to the Local Calderón Problem by Means of the Caffarelli-Silvestre Extension
Giovanni Covi, Tuhin Ghosh, Angkana Rüland +1
We relate the (anisotropic) variable coefficient local and nonlocal Calderón problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichl…
The Calderón problem for nonlocal parabolic operators
Ching-Lung Lin, Yi-Hsuan Lin, Gunther Uhlmann
We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time d…
Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data
Sombuddha Bhattacharyya, Maarten V. de Hoop, Vitaly Katsnelson +1
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we a…
The geodesic X-ray transform with matrix weights
Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann +1
Consider a compact Riemannian manifold of dimension with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ra…