Partial Data Calderón Problems for L^n/2 Potentials on Admissible Manifolds

2018/05/22 by Leo Tzou, Tzou, Leo
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques #math.AP

paper · pdf · doi:10.48550/arxiv.1805.09161

Clarified the last section. Removed redundancies

openalex publication_date 2018/05/22 · openalex created_date 2018/06/01 · arxiv created 2018/08/18 · arxiv updated 2018/08/21 · openalex updated_date 2026/07/28

Abstract

We solve the partial data Calderón problem on conformally transversallly anisotropic (CTA) manifolds with L^n/2 potentials - on par with sharp unique continuation result of \citeJerKen. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sjöstrand-Uhlmann \citeksu. This is done by constructing a "Green's function" which possesses both desirable boundary conditions \em and satisfies semiclassical type estimates in the suitable L^p spaces. No Carleman estimates were used in the writing of this article which makes it starkly different from the traditional approaches based on \citeBukUhl and \citeksu.

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