Stability estimates in tensor tomography

Stability estimates in tensor tomography Full article

Journal

Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345

Output data

Year: 2018, Volume: 12, Number: 5, Pages: 1245-1262 Pages count : 18 DOI: 10.3934/ipi.2018052

Tags

Tensor tomography; The Dirichlet principle; The Korn inequality; X-ray transform

Authors

Boman J. ¹ , Sharafutdinov V. ^2,3

Affiliations

1	Department of Mathematics, Stockholm University, Stockholm, 106 91, Sweden
2	Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State University, 2 Pirogov street, Novosibirsk, 630090, Russian Federation

We study the X-ray transform I of symmetric tensor fields on a smooth convex bounded domain Ω ⊂ ℝn. The main result is the stability estimate (Formula Presented), where sf is the solenoidal part of the tensor field f. The proof is based on a comparison of the Dirichlet integrals for the exterior and interior Dirichlet problems and on a generalization of the Korn inequality to symmetric tensor fields of arbitrary rank. © 2018 American Institute of Mathematical Sciences.

Boman J. , Sharafutdinov V.
Stability estimates in tensor tomography
Inverse Problems and Imaging. 2018. V.12. N5. P.1245-1262. DOI: 10.3934/ipi.2018052 WOS Scopus OpenAlex

Web of science:	WOS:000446988400009
Scopus:	2-s2.0-85052247364
OpenAlex:	W2887530441

DB	Citing
Scopus	10
OpenAlex	14
Web of science	11