2 papers
math.AP2025
Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle
Jiahuan Li, Zhichen Ying
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 low…
math.AP2025
Nadirashvili' Conjecture for Elliptic PDEs and its Applications
Jiahuan Li, Junyuan Wang, Zhichen Ying
In this article, we investigate the conjecture posed by Nadirashvili in 1997. It states that if a harmonic function has bounded nodal volume in the unit ball, then the supermum ove…