The $L^p$ Carleman estimate and a partial data inverse problem
| Autor: | Chung, Francis J., Tzou, Leo |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We construct an explicit Green's function for the conjugated Laplacian $e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial data inverse problem for the Schr\"odinger equation with potential $q \in L^{n/2}$. We also use this Green's function to derive $L^p$ Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \cite{krs}, but for functions with support up to part of the boundary. Comment: 33 pages plus appendix and references |
| Databáze: | arXiv |
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