Stability of inverse problems in an infinite slab with partial data

TL;DR

This paper investigates the stability of inverse boundary value problems in an infinite slab with partial data, providing a log-log stability estimate for the Schrödinger equation, extending previous uniqueness results.

Contribution

It quantifies the uniqueness method for inverse problems in an infinite slab and establishes a new stability estimate for Schrödinger equations with partial boundary data.

Findings

Proves a log-log stability estimate for inverse Schrödinger problems

Quantifies the method of uniqueness for inverse boundary problems

Extends stability analysis to partial data scenarios in an infinite slab

Abstract

In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and Uhlmann for the case of the magnetic Schrodinger equation. Here we quantify the method of uniqueness proposed by Li and Uhlmann and prove a log-log stability estimate for the inverse problems associated to the Schrodinger equation. The boundary measurements considered in these problems are modelled by partial knowledge of the Dirichlet-to-Neumann map: in the first inverse problem, the corresponding Dirichlet and Neumann data are known on different boundary hyperplanes of the slab; in the second inverse problem, they are known on the same boundary hyperplane of the slab.