Upper bounds of nodal sets for solutions of bi-Laplace equations: II
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915835582349312 |
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| author | Zhu, Jiuyi |
| author_facet | Zhu, Jiuyi |
| contents | We investigate the upper bounds of nodal sets for solutions of bi-Laplace equations without using frequency functions which play an essential role in the study of nodal sets in the celebrated work by Logunov \cite{Lo18}. We obtain some delicate monotonicity and propagation of smallness results by Carleman estimates. A polynomial upper bound for the nodal sets of solutions is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04677 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Upper bounds of nodal sets for solutions of bi-Laplace equations: II Zhu, Jiuyi Analysis of PDEs We investigate the upper bounds of nodal sets for solutions of bi-Laplace equations without using frequency functions which play an essential role in the study of nodal sets in the celebrated work by Logunov \cite{Lo18}. We obtain some delicate monotonicity and propagation of smallness results by Carleman estimates. A polynomial upper bound for the nodal sets of solutions is obtained. |
| title | Upper bounds of nodal sets for solutions of bi-Laplace equations: II |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.04677 |