Mathematical Research Letters

Volume 16 (2009)

Number 6

On the linearized local Calderón problem

Pages: 955 – 970

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n6.a4

Authors

David Dos Santos Ferreira (Université Paris 13)

Carlos E. Kenig (University of Chicago)

Johannes Sjöstrand (Université de Bourgogne)

Gunther Uhlmann (University of Washington)

Abstract

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}.

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