Stability estimates for the relativistic Schrödinger equation from partial boundary data. (3rd December 2020)

• Record Type: Journal Article
• Authors: Senapati, Soumen
• Is Part Of: Inverse problems. Volume 37:Number 1(2021)
• Publication Date: 2020-12-03
• Subjects: hyperbolic inverse problem -- stability estimate -- time-dependent coefficient -- partial boundary data; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abca7f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We derive stability estimates for the determination of time-dependent vector and scalar potentials in the relativistic Schrödinger equation from partial boundary data. For the case of space dimensions at least 3, we obtain log–log stability estimates for the determination of vector potentials (modulo gauge equivalence) and log–log–log stability estimates for the determination of scalar potentials from partial boundary data assuming suitable a priori bounds on these potentials.