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    On increasing stability of the continuation for elliptic equations of second order without (Pseudo)convexity assumptions

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    Date
    2019-10
    Author
    Isakov, Victor
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    Citation
    Victor Isakov. On increasing stability of the continuation for elliptic equations of second order without (pseudo)convexity assumptions. Inverse Problems & Imaging, 2019, 13 (5) : 983-1006
    Abstract
    We derive bounds of solutions of the Cauchy problem for general elliptic partial differential equations of second order containing parameter (wave number) k which are getting nearly Lipschitz for large k. Proofs use energy estimates combined with splitting solutions into low and high frequencies parts, an associated hyperbolic equation and the Fourier-Bros-Iagolnitzer transform to replace the hyperbolic equation with an elliptic equation without parameter k. The results suggest a better resolution in prospecting by various (acoustic, electromagnetic, etc) stationary waves with higher wave numbers without any geometric assumptions on domains and observation sites.
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    URI
    https://doi.org/10.3934/ipi.2019044
    http://hdl.handle.net/10057/16799
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