We consider two inverse problems for the multi-channel two-dimensional Schrödinger equation at fixed positive energy, i.e., the equation-Δψ+V (x)ψ=Eψ at fixed positive E, where V is a matrix-valued potential. The first is the Gel'fand inverse problem on a bounded domain D at fixed energy and the second is the inverse fixed-energy scattering problem on the whole plane. We present in this paper two algorithms which give efficient approximate solutions to these problems: in particular, in both cases, we show that the potential V is reconstructed with Lipschitz stability by these algorithms up to O(E-(m-2)/2) in the uniform norm as, under the assumptions that V is m-times differentiable in L1, for m≥3, and has sufficient boundary decay. © 2012 The Author(s).

Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems

SANTACESARIA, MATTEO
2013-01-01

Abstract

We consider two inverse problems for the multi-channel two-dimensional Schrödinger equation at fixed positive energy, i.e., the equation-Δψ+V (x)ψ=Eψ at fixed positive E, where V is a matrix-valued potential. The first is the Gel'fand inverse problem on a bounded domain D at fixed energy and the second is the inverse fixed-energy scattering problem on the whole plane. We present in this paper two algorithms which give efficient approximate solutions to these problems: in particular, in both cases, we show that the potential V is reconstructed with Lipschitz stability by these algorithms up to O(E-(m-2)/2) in the uniform norm as, under the assumptions that V is m-times differentiable in L1, for m≥3, and has sufficient boundary decay. © 2012 The Author(s).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1018563
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