Global uniqueness for a two-dimensional semilinear elliptic inverse problem

Isakov, Victor; Nachman, Adrian I.

doi:10.1090/S0002-9947-1995-1311909-1

Global uniqueness for a two-dimensional semilinear elliptic inverse problem
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by Victor Isakov and Adrian I. Nachman PDF

Trans. Amer. Math. Soc. 347 (1995), 3375-3390 Request permission

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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