On the linearized local Calderon problem

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 $n\ge 2$. This is proved using ideas coming from the proof of Kashiwara's Watermelon theorem.

References in corpus (2)

• Global uniqueness from partial Cauchy data in two dimensions
• Partial Data for the Calderon Problem in Two Dimensions