Translator Disclaimer
2020 The Calderón problem for the fractional Schrödinger equation
Tuhin Ghosh, Mikko Salo, Gunther Uhlmann
Anal. PDE 13(2): 455-475 (2020). DOI: 10.2140/apde.2020.13.455

Abstract

We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension 1 and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calderón problem.

Citation

Download Citation

Tuhin Ghosh. Mikko Salo. Gunther Uhlmann. "The Calderón problem for the fractional Schrödinger equation." Anal. PDE 13 (2) 455 - 475, 2020. https://doi.org/10.2140/apde.2020.13.455

Information

Received: 9 July 2018; Revised: 8 November 2018; Accepted: 23 February 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07181507
MathSciNet: MR4078233
Digital Object Identifier: 10.2140/apde.2020.13.455

Subjects:
Primary: 26A33 , 35J10 , 35R30
Secondary: 35J70

Keywords: ‎approximation property‎‎ , Calderón problem , fractional Laplacian , inverse problem

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.13 • No. 2 • 2020
MSP
Back to Top