A uniqueness theorem for inverse problems in quasilinear anisotropic media II
Kholil, Md Ibrahim Sun, Ziqi
Kholil, Md Ibrahim
Sun, Ziqi
Citations
Altmetric:
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2024-02
Type
Article
Genre
Keywords
Quasilinear,Regularity,Dirichlet to Neumann map,Elliptic equation,Linearization,Riemannian manifold,Conformal diffeomorphism
Subjects (LCSH)
Citation
Md Ibrahim Kholil, Ziqi Sun. A uniqueness theorem for inverse problems in quasilinear anisotropic media II. Inverse Problems and Imaging, 2024, 18(1): 104-112. doi: 10.3934/ipi.2023024
Abstract
We study the question of whether one can uniquely determine scalar quasilinear conductivity in an anisotropic medium by making voltage and current measurements at the boundary. We prove a global uniqueness in the C$^{2,α}$ category, by showing that the C$^{2,α}$ quasilinear conductivity in an anisotropic medium can be uniquely determined by the voltage and current measurements at the boundary, i.e., by the Dirichlet to Neumann map, assuming that an anisotropic linear conductivity can be identified by its Dirichlet to Neumann map up to a diffeomorphism that fixes the boundary.
Table of Contents
Description
Click on the DOI link to access this article (may not be free).
Publisher
American Institute of Mathematical Sciences
Journal
Inverse Problems and Imaging
Book Title
Series
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
DOI
ISSN
1930-8337