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Transactions of the American Mathematical Society

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Global uniqueness for a two-dimensional semilinear elliptic inverse problem

Authors: Victor Isakov and Adrian I. Nachman
Journal: Trans. Amer. Math. Soc. 347 (1995), 3375-3390
MSC: Primary 35R30; Secondary 35J60
MathSciNet review: 1311909
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Abstract: For a general class of nonlinear Schrödinger equations $ - \Delta u + a(x,u) = 0$ in a bounded planar domain $ \Omega $ we show that the function $ a(x,u)$ can be recovered from knowledge of the corresponding Dirichlet-to-Neumann map on the boundary $ \partial \Omega $.

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