A1 Journal article (refereed)
Uniqueness in an inverse problem of fractional elasticity (2023)

Covi, G., de Hoop, M., & Salo, M. (2023). Uniqueness in an inverse problem of fractional elasticity. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 479(2278), Article 20230474. https://doi.org/10.1098/rspa.2023.0474

JYU authors or editors

Publication details

All authors or editors: Covi, Giovanni; de Hoop, Maarten; Salo, Mikko

Journal or series: Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences

ISSN: 1364-5021

eISSN: 1471-2946

Publication year: 2023

Volume: 479

Issue number: 2278

Article number: 20230474

Publisher: The Royal Society

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1098/rspa.2023.0474

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/90188

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2209.15316

Abstract

We study a nonlinear inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated with a linear, isotropic fractional elasticity operator from fractional Dirichlet-to-Neumann data. In our analysis, we make use of a fractional matrix Schrödinger equation via a generalization of the so-called Liouville reduction to the case of fractional elasticity. We conclude that unique recovery is possible if the Lamé parameters agree and are constant in the exterior, and their Poisson ratios agree everywhere. Our study is motivated by the significant recent activity in the field of nonlocal elasticity.

Keywords: inverse problems; partial differential equations; elasticity (physical properties)

Free keywords: nonlocal operators; fractional Calderón problem; inverse problems; fractional elasticity; isotropic elasticity

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2023

Preliminary JUFO rating: 2