79 citations · 82 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
Rigidity of broken geodesic flow and inverse problems
Yaroslav Kurylev, Matti Lassas, Gunther Uhlmann
Consider a broken geodesics on a compact Riemannian manifold with boundary of dimension . The broken geodesics are unions of two geodesics with the prop…