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

2016/10/06 by Francis J. Chung, Chung, Francis J., Leo Tzou +1 · 1 citation
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics

paper · pdf · doi:10.48550/arxiv.1610.01715

Abstract

We construct an explicit Green's function for the conjugated Laplacian e^{-ω⋅ x/h}Δe^{-ω⋅ 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 ∈ L^n/2. We also use this Green's function to derive L^p Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \citekrs, but for functions with support up to part of the boundary.

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