A density property for tensor products of gradients of harmonic functions and applications

Cătălin I. Cârstea*, Ali Feizmohammadi

*此作品的通信作者

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

We show that linear combinations of tensor products of k gradients of harmonic functions, with k at least three, are dense in C(Ω‾), for any bounded domain Ω in dimension 3 or higher. The bulk of the argument consists in showing that any smooth compactly supported k-tensor that is L2-orthogonal to all such products must be zero. This is done by using a Gaussian quasi-mode based construction of harmonic functions in the orthogonality relation. We then demonstrate the usefulness of this result by using it to prove uniqueness in the inverse boundary value problem for a coupled quasilinear elliptic system. The paper ends with a discussion of the corresponding property for products of two gradients of harmonic functions, and the connection of this property with the linearized anisotropic Calderón problem.

原文English
文章編號109740
期刊Journal of Functional Analysis
284
發行號2
DOIs
出版狀態Published - 15 1月 2023

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