Increasing stability of the inverse boundary value problem for the Schrödinger equation

2013/02/05 by V Isakov, S Nagayasu, Isakov, V +5 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35R30 #Secondary 65N21 #math.AP #msc:35R30 #msc:65N21

paper · pdf · doi:10.48550/arxiv.1302.0940

arxiv created 2013/02/05 · arxiv updated 2013/02/06

Abstract

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schrödinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of the wave number (or energy). The main contribution of this work is to provide a unified and easier approach to the same problem based on the complex geometrical optics solutions.

Cited by

• Stability for the inverse random potential scattering problem

Related

• Stability of inverse boundary value problem for the fourth-order Schrödinger equation
• Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map
• Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds
• Increasing stability for the conductivity and attenuation coefficients
• Inverse boundary value problem for Schrödinger equation in two dimensions