Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle

Jiahuan Li; Zhichen Ying

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arXiv · 2512.12305

Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle

Jiahuan Li·Zhichen Ying

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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.

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BibTeX RIS

Jiahuan Li, Zhichen Ying. 2025-12-13. Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle. https://arxiv.org/abs/2512.12305

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