Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map

Victor Isakov; Jenn-Nan Wang

doi:10.3934/ipi.2014.8.1139

Article Contents

2014, Volume 8, Issue 4: 1139-1150. Doi: 10.3934/ipi.2014.8.1139

This issue Previous Article Calderón problem for Maxwell's equations in cylindrical domain Next Article The nonlinear Fourier transform for two-dimensional subcritical potentials

Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map

Victor Isakov^1, and
Jenn-Nan Wang^2,

1.
Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS 67260-0033
2.
Institute of Applied Mathematics, NCTS (Taipei), National Taiwan University, Taipei 106

Received: September 2013

Revised: January 2014

Published online: November 2014

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Abstract

We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schrödinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when energy level/frequency is growing. These bounds hold under certain a-priori regularity constraints on the unknown coefficient. Proofs use complex and bounded complex geometrical optics solutions.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J10, 35Q40, 35E05, 81Q15.

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