Inverse problems for a fractional conductivity equation
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.
Main Author
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Pergamon Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202002122058Use this for linking
Review status
Peer reviewed
ISSN
0362-546X
DOI
https://doi.org/10.1016/j.na.2019.01.008
Language
English
Published in
Nonlinear Analysis: Theory, Methods and Applications
Citation
- Covi, G. (2020). Inverse problems for a fractional conductivity equation. Nonlinear Analysis: Theory, Methods and Applications, 193, 111418. https://doi.org/10.1016/j.na.2019.01.008
License
Funder(s)
European Commission
Funding program(s)
ERC Consolidator Grant
ERC Consolidator Grant
Additional information about funding
This work is part of the PhD research of the author. The author was partially supported by the European Research Council under Horizon 2020 (ERC CoG 770924). The author wishes to dearly thank professor M. Salo for his precious ideas and helpful discussion in the making of this work.
Copyright©2019 The Author(s)