275 citations · 957 across the 58 of their papers we have counts for
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On an inverse boundary value problem for a nonlinear elastic wave equation
Gunther Uhlmann, Jian Zhai
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y].…
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
Katya Krupchyk, Gunther Uhlmann
We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain which vanish on a closed proper sub…
Generic uniqueness and stability for the mixed ray transform
Maarten V. de Hoop, Teemu Saksala, Gunther Uhlmann +1
We consider the mixed ray transform of tensor fields on a three-dimensional compact simple Riemannian manifold with boundary. We prove the injectivity of the transform, up to natur…
The Light Ray transform on Lorentzian manifolds
Matti Lassas, Lauri Oksanen, Plamen Stefanov +1
We study the weighted light ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze as a Fourier Integral Operator and show tha…
A remark on partial data inverse problems for semilinear elliptic equations
Katya Krupchyk, Gunther Uhlmann
We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in , , for a class of semilinear elliptic…
Recovery of discontinuous Lamé parameters from local dynamic boundary data
Peter Caday, Maarten V. de Hoop, Vitaly Katsnelson +1
Consider an isotropic elastic medium whose Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solutio…