Inverse problems for a fractional conductivity equation. (April 2020)

• Record Type: Journal Article
• Authors: Covi, Giovanni
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: 35R11 -- 35R30; Fractional conductivity equation -- Non-local operators -- Inverse problems -- Calderón problem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrödinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.