Abstract
In 1995, Tataru proved a Carleman-type estimate for linear operators with partially analytic coefficients that is generally used to prove the unique continuation of those operators. In this paper, we use this inequality to study the stability of the unique continuation in the case of the wave equation with coefficients independent of time. We prove a logarithmic estimate in a ball whose radius has an explicit dependence on the C1-norm of the coefficients and on the other geometric properties of the operator.
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R. B. was supported by the postdoc programme of the Hausdorff Center for Mathematics in Bonn and by the AXA Mittag-Leffler Fellowship Project, funded by the AXA Research Fund.
Y. K. and R. B. were partly supported by EPSRC.
M. L. and R. B. were partly supported by the Academy of Finland, CoE-project 250215 and project 273979.
This work was partly done at the Isaac Newton Institute forMathematical Sciences and the Mittag-Leffler Institute.
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Bosi, R., Kurylev, Y. & Lassas, M. Stability of the unique continuation for the wave operator via Tataru inequality: the local case. JAMA 134, 157–199 (2018). https://doi.org/10.1007/s11854-018-0006-2
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DOI: https://doi.org/10.1007/s11854-018-0006-2