Increasing stability for determining the potential in the Schr\"odinger equation with attenuation from the Dirichlet-to-Neumann map

TL;DR

This paper demonstrates increasing stability in recovering the potential in the Schrödinger equation with attenuation from boundary measurements as the energy level increases, under certain regularity conditions.

Contribution

It provides new bounds indicating increasing stability in the inverse Schrödinger problem with attenuation at high energies, using complex geometrical optics solutions.

Findings

Stability bounds improve with higher energy levels.

Results depend on regularity constraints of the potential.

Uses complex geometrical optics solutions for proofs.

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 Schr\"odinger 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.