Local analytic regularity in the linearized Calderón problem

Abstract

We consider the linearization of the Dirichlet-to-Neumann (DN) map as a function of the potential. We show that it is injective at a real analytic potential for measurements made at an open subset of analyticity of the boundary. More generally, we relate the analyticity up to the boundary of the variations of the potential to the analyticity of the symbols of the corresponding variations of the DN-map.

A gap in the proof of Lemma 1.2 in v1 prompted us to remove that lemma, causing a superficial change in the formulation of the main result

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