Proves that the Dirichlet-to-Neumann map for convex solutions of det D²u = f(x) uniquely determines positive f, by reducing the inverse problem to injectivity of the Euclidean X-ray transform via large boundary values.
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An inverse source problem for the Monge--Ampere equation from large boundary data
Proves that the Dirichlet-to-Neumann map for convex solutions of det D²u = f(x) uniquely determines positive f, by reducing the inverse problem to injectivity of the Euclidean X-ray transform via large boundary values.