On the linearized local Calderón problem

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 ≥ 2. This is proved using ideas coming from the proof of Kashiwara’s Watermelon theorem [14]. Contents