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Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality

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Abstract

The authors prove Carleman estimates for the Schrödinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining L p-potentials. An L 2-level observability inequality and unique continuation results for the Schrödinger equation are also obtained.

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Correspondence to Ganghua Yuan.

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Project supported by the Japanese Government Scholarship, the National Natural Science Foundation of China (No. 10801030), the Science Foundation for Young Teachers of Northeast Normal University (No. 20080103), the Japan Society for the Promotion of Science (No. 15340027) and the Grant from the Ministry of Education, Cultures, Sports and Technology of Japan (No. 17654019).

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Yuan, G., Yamamoto, M. Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality. Chin. Ann. Math. Ser. B 31, 555–578 (2010). https://doi.org/10.1007/s11401-010-0585-4

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  • DOI: https://doi.org/10.1007/s11401-010-0585-4

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