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STABILITY ESTIMATES IN TENSOR TOMOGRAPHY
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22018 (English)In: Inverse Problems and Imaging, ISSN 1930-8337, E-ISSN 1930-8345, Vol. 12, no 5, p. 1245-1262Article in journal (Refereed) Published
Abstract [en]

We study the X-ray transform I of symmetric tensor fields on a smooth convex bounded domain Omega C R-n. The main result is the stability estimate parallel to(s)f parallel to(L2) <= C parallel to If parallel to(H1/2), where (s)f 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.

Place, publisher, year, edition, pages
2018. Vol. 12, no 5, p. 1245-1262
Keywords [en]
Tensor tomography, X-ray transform, the Dirichlet principle, the Korn inequality
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-162016DOI: 10.3934/ipi.2018052ISI: 000446988400009OAI: oai:DiVA.org:su-162016DiVA, id: diva2:1263699
Available from: 2018-11-16 Created: 2018-11-16 Last updated: 2018-11-16Bibliographically approved

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