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

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 Schrödinger 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.

33 pages plus appendix and references

References in corpus (1)

• Partial Data Inverse Problems for Maxwell Equations via Carleman Estimates

Cited by in corpus (1)

• Determination of singular time-dependent coefficients for wave equations from full and partial data