On the linearized local Calderon problem

2009/05/05 by D. Dos Santos Ferreira, C. E. Kenig, Ferreira, D. Dos Santos +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.0905.0530

arxiv created 2009/05/05 · arxiv updated 2009/12/01

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 Ω vanishing on any fixed closed proper subset of the boundary are dense in L¹(Ω) in all dimensions n ≥ 2. This is proved using ideas coming from the proof of Kashiwara's Watermelon theorem.

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