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arXiv · 2608.08866

Quantitative uniqueness for bi-Laplace equations with potentials

Long Teng·Zhiwei Wang·Jiuyi Zhu
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Abstract

We study quantitative unique continuation for bi-Laplace equations \[\Delta^{2}u+V(x)u=0 \] by introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and H\"older continuous potentials. Three-ball inequalities are built on rescaling invariant weighted frequency functions. The vanishing order results are shown by related, but different weighted frequency functions.

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Long Teng, Zhiwei Wang, Jiuyi Zhu. 2026-08-09. Quantitative uniqueness for bi-Laplace equations with potentials. https://arxiv.org/abs/2608.08866

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