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arXiv · 2603.04677

Upper bounds of nodal sets for solutions of bi-Laplace equations: II

Jiuyi Zhu
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Abstract

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.

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Jiuyi Zhu. 2026-03-04. Upper bounds of nodal sets for solutions of bi-Laplace equations: II. https://arxiv.org/abs/2603.04677

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