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

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 \cite{JerKen}. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sjöstrand-Uhlmann \cite{ksu}. 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 \cite{BukUhl} and \cite{ksu}.

Clarified the last section. Removed redundancies

References in corpus (1)

• The Calderon problem with partial data on manifolds and applications