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Stability estimates in tensor tomography

  • * Corresponding author: Vladimir Sharafutdinov

    * Corresponding author: Vladimir Sharafutdinov
The second author was supported by RFBR, Grant 17-51-150001.
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  • 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.

    Mathematics Subject Classification: Primary: 44A15, 35J20; Secondary: 74B05.


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