Standard

Stability estimates in tensor tomography. / Boman, Jan; Sharafutdinov, Vladimir.

In: Inverse Problems and Imaging, Vol. 12, No. 5, 10.2018, p. 1245-1262.

Research output: Contribution to journal › Article › peer-review

Harvard

Boman, J & Sharafutdinov, V 2018, 'Stability estimates in tensor tomography', Inverse Problems and Imaging, vol. 12, no. 5, pp. 1245-1262. https://doi.org/10.3934/ipi.2018052

APA

Boman, J., & Sharafutdinov, V. (2018). Stability estimates in tensor tomography. Inverse Problems and Imaging, 12(5), 1245-1262. https://doi.org/10.3934/ipi.2018052

Vancouver

Boman J, Sharafutdinov V. Stability estimates in tensor tomography. Inverse Problems and Imaging. 2018 Oct;12(5):1245-1262. doi: 10.3934/ipi.2018052

Author

Boman, Jan ; Sharafutdinov, Vladimir. / Stability estimates in tensor tomography. In: Inverse Problems and Imaging. 2018 ; Vol. 12, No. 5. pp. 1245-1262.

BibTeX

@article{aa4f697d4d0b4a34855fabd7059f8bfe,
title = "Stability estimates in tensor tomography",
abstract = "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.",
keywords = "Tensor tomography, The Dirichlet principle, The Korn inequality, X-ray transform, the Dirichlet principle, the Korn inequality",
author = "Jan Boman and Vladimir Sharafutdinov",
year = "2018",
month = oct,
doi = "10.3934/ipi.2018052",
language = "English",
volume = "12",
pages = "1245--1262",
journal = "Inverse Problems and Imaging",
issn = "1930-8337",
publisher = "American Institute of Mathematical Sciences",
number = "5",

}

RIS

TY - JOUR

T1 - Stability estimates in tensor tomography

AU - Boman, Jan

AU - Sharafutdinov, Vladimir

PY - 2018/10

Y1 - 2018/10

N2 - 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.

AB - 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.

KW - Tensor tomography

KW - The Dirichlet principle

KW - The Korn inequality

KW - X-ray transform

KW - the Dirichlet principle

KW - the Korn inequality

UR - http://www.scopus.com/inward/record.url?scp=85052247364&partnerID=8YFLogxK

U2 - 10.3934/ipi.2018052

DO - 10.3934/ipi.2018052

M3 - Article

AN - SCOPUS:85052247364

VL - 12

SP - 1245

EP - 1262

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 5

ER -

ID: 16336502