Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle
Analysis of PDEs
2025-12-23 v2
Abstract
In this note, we first try to prove a uniform lower bound of nodal volume in elliptic homogenization setting. This lower bound is far from optimal. But, we can prove a constant lower bound in dimension two. Motivated by the proof, we extend this results to more general settings. To be more specific, we prove that the nodal volume has a constant lower bound for all continuous functions with strong maximum principle. Our result works for general functions beyond solutions to elliptic PDEs.
Cite
@article{arxiv.2512.12305,
title = {Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle},
author = {Jiahuan Li and Zhichen Ying},
journal= {arXiv preprint arXiv:2512.12305},
year = {2025}
}