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

Cătălin I. Cârstea*, Ali Feizmohammadi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number109740
JournalJournal of Functional Analysis
Volume284
Issue number2
DOIs
StatePublished - 15 Jan 2023

Keywords

  • Gradients of harmonic functions
  • Inverse problems
  • Quasilinear elliptic systems

Fingerprint

Dive into the research topics of 'A density property for tensor products of gradients of harmonic functions and applications'. Together they form a unique fingerprint.

Cite this