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arXiv · 1610.01715

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

Francis J. Chung·Leo Tzou
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Abstract

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.

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Francis J. Chung, Leo Tzou. 2016-10-06. The $L^p$ Carleman estimate and a partial data inverse problem. https://arxiv.org/abs/1610.01715

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