The $L^p$ Carleman estimate and a partial data inverse problem

Autor: Chung, Francis J., Tzou, Leo
Rok vydání: 2016
Předmět:
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