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arXiv · 0905.0530

On the linearized local Calderon problem

D. Dos Santos Ferreira·C. E. Kenig·J. Sjoestrand·G. Uhlmann
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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 $L^{1}(Ω)$ in all dimensions $n \geq 2$. This is proved using ideas coming from the proof of Kashiwara's Watermelon theorem.

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D. Dos Santos Ferreira, C. E. Kenig, J. Sjoestrand, G. Uhlmann. 2009-05-05. On the linearized local Calderon problem. https://arxiv.org/abs/0905.0530

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