A Regularity Theory for Stationary Two-valued Harmonic Functions
Analysis of PDEs
2025-05-19 v2
Abstract
For stationary two-valued harmonic functions with H\"older regularity, we establish their Lipschitz regularity and prove that the nodal set consists of analytic hypersurfaces away from a singular set. The main tools are the Almgren monotonicity formula and the blow-up method. These results are applicable to some limiting problems in segregation models.
Cite
@article{arxiv.2503.23318,
title = {A Regularity Theory for Stationary Two-valued Harmonic Functions},
author = {Lingxiao Cheng and Lubo Wang},
journal= {arXiv preprint arXiv:2503.23318},
year = {2025}
}
Comments
The main result of this paper has already been proved in [Tavares-Terracini, CVPDE, 2012] and [Tavares-Terracini-Verzini, CPAM, 2010], corresponding to reference [32] here and the reference therein