On the linearized local Calderon problem

Ferreira, D. Dos Santos; Kenig, C. E.; Sjoestrand, J.; Uhlmann, G.

On the linearized local Calderon problem

Authors

Ferreira, D. Dos Santos

Kenig, C. E.

Sjoestrand, J.

Uhlmann, G.

Description

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 $Ω$ vanishing on any fixed closed proper subset of the boundary are dense in $L^{1}(Ω)$ in all dimensions $n \geq 2$. This is proved using ideas coming from the proof of Kashiwara's Watermelon theorem.