Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908724555153408 |
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| author | Li, Jiahuan Ying, Zhichen |
| author_facet | Li, Jiahuan Ying, Zhichen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle Li, Jiahuan Ying, Zhichen Analysis of PDEs 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. |
| title | Lower Bound of Nodal Sets in Elliptic Homogenization and Functions with Strong Maximum Principle |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.12305 |