Increasing stability of the inverse boundary value problem for the Schr\"odinger equation

TL;DR

This paper investigates the increasing stability phenomenon in the inverse boundary value problem for the Schrödinger equation, offering a unified approach using complex geometrical optics solutions to improve understanding across different energy ranges.

Contribution

It introduces a simplified, unified method based on complex geometrical optics solutions to analyze increasing stability in the Schrödinger inverse problem.

Findings

Provides a unified framework for stability analysis

Enhances understanding of stability across energy ranges

Simplifies previous approaches using complex geometrical optics

Abstract

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger 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.