Conjugate harmonic functions in 3D with respect to a unitary gradient
Analysis of PDEs
2025-02-14 v1 Classical Analysis and ODEs
Optimization and Control
Abstract
We propose to relax the classic Cauchy-Riemann equations for a mapping. We support the interest of such a proposal by looking at one specific situation in 3D, and proving the existence of pairs of harmonic conjugate functions with respect to a unitary gradient as the title of this contribution conveys. We further investigate the relationship between boundary conditions for such pairs, the importance of the unitary constraint, and the eventual link of these ideas to Calder\'on's problem in 3D.
Cite
@article{arxiv.2502.09034,
title = {Conjugate harmonic functions in 3D with respect to a unitary gradient},
author = {Pablo Pedregal},
journal= {arXiv preprint arXiv:2502.09034},
year = {2025}
}
Comments
15 pages