# American Institute of Mathematical Sciences

October  2018, 12(5): 1245-1262. doi: 10.3934/ipi.2018052

## Stability estimates in tensor tomography

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

Received  October 2017 Published  July 2018

Fund Project: The second author was supported by RFBR, Grant 17-51-150001.

We study the X-ray transform $I$ of symmetric tensor fields on a smooth convex bounded domain $Ω\subset{\mathbb R}^n$. The main result is the stability estimate $\|^{s}f\|_{L^2}≤ C\|If\|_{H^{1/2}}$, 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.

Citation: Jan Boman, Vladimir Sharafutdinov. Stability estimates in tensor tomography. Inverse Problems & Imaging, 2018, 12 (5) : 1245-1262. doi: 10.3934/ipi.2018052
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