Geodesic
Reconstruction of a second rank tensor field with zero trace from incomplete data
Daghestan Electronic Mathematical Reports, no. 14 (2020), pp. 38-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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An algorithm for the complete reconstruction of a tensor field of rank 2 in three-dimensional Euclidean space on incomplete integral data is constructed. The solenoid part of the field is constructed using linear integrals on straight lines that intersect a curve at infinity, and the displacement field is constructed using the traceless normal ray integrals.
Keywords: ray transform, second-rank tensor field, Saint-Venant operator, displacement field, traceless normal part.
Mots-clés : reconstruction 
@article{DEMR_2020_14_a3,
     author = {Z. G. Medzhidov},
     title = {Reconstruction of a second rank tensor field with zero trace from incomplete data},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {38--47},
     year = {2020},
     number = {14},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2020_14_a3/}
}
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Z. G. Medzhidov. Reconstruction of a second rank tensor field with zero trace from incomplete data. Daghestan Electronic Mathematical Reports, no. 14 (2020), pp. 38-47. http://geodesic.mathdoc.fr/item/DEMR_2020_14_a3/

[1] Palamodov V.P., “On reconstruction of strain fields from tomographic data”, ID 85002, Inverse Problems, 31:8 (2015), 12 | DOI | MR | Zbl

[2] Palamodov V.P., “Reconstruction of a differential form from Doppler transform”, SIAM J. Math. Anal, 2009, no. 41, 1713–1720 | DOI | MR | Zbl

[3] Medzhidov Z.G., “Obraschenie luchevogo preobrazovaniya simmetrichnogo tenzornogo polya s istochnikami na krivoi”, Vestnik DGU, 2013, no. 6, 107–113

[4] Medzhidov Z.G., “Obraschenie luchevogo preobrazovaniya tenzornykh polei s beskonechno udalennymi istochnikami”, Vestnik DGU, 2015, no. 1, 19–26

[5] Medzhidov Z.G., “Formuly obrascheniya tenzornoi tomografii po nepolnym dannym”, DEMI, 2014, no. 2, 75–86

[6] Sharafutdinov V.A., Integralnaya geometriya tenzornykh polei, Nauka, Novosibirsk, 1993, 233 pp. | MR