On the linearized local Calderon problem

Details On the linearized local Calderon problem On the linearized local Calderon problem

2009-05-05

arxiv.org/abs/0905.0530v1

Mathematics

Analysis of PDEs

Scientific paper

In this article, we investigate a density problem coming from the linearization of Calder\'on'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.

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