Mathematical Research Letters

Volume 16 (2009)

Number 6

On the linearized local Calderón problem

Pages: 955 – 970



David Dos Santos Ferreira (Université Paris 13)

Carlos E. Kenig (University of Chicago)

Johannes Sjöstrand (Université de Bourgogne)

Gunther Uhlmann (University of Washington)


In this article, we investigate a density problem coming from the linearization of Calderón’s problem with partial data. More precisely, we prove that the set of products of harmonic functions on a bounded smooth domain $\Omega$ vanishing on any fixed closed proper subset of the boundary are dense in $L^{1}(\Omega)$ in all dimensions $n \geq 2$. This is proved using ideas coming from the proof of Kashiwara’s Watermelon theorem \cite{K}.

Published 1 January 2009