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| Carleman Estimates for the Schr¨odinger Equation and Applications to an Inverse Problem and an Observability Inequality |
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Citation： |
Ganghua YUAN,Masahiro YAMAMOTO.Carleman Estimates for the Schr¨odinger Equation and Applications to an Inverse Problem and an Observability Inequality[J].Chinese Annals of Mathematics B,2010,31(4):555~578 |
| Page view： 2020
Net amount： 1706 |
Authors： |
Ganghua YUAN; Masahiro YAMAMOTO; |
Foundation： |
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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| Abstract： |
The authors prove Carleman estimates for the Schr{\"o}dinger
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 Schr{\"o}dinger equation are also obtained. |
Keywords： |
Schr¨odinger equation, Carleman estimate, Observability inequality,
Inverse problem, Unique continuation |
Classification： |
93B05, 35R30, 35B60 |
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