AI 中文总结
该研究针对带势函数的双调和方程，引入新的加权频率函数建立定量三球不等式与消失阶界，解决其定量唯一延拓问题。
AI 中文摘要
我们通过引入若干新的加权频率函数，研究带势函数V(x)的双调和方程Δ²u+V(x)u=0的定量唯一延拓问题。针对有界且Hölder连续的势函数，我们建立了定量三球不等式与消失阶界；三球不等式基于重标度不变的加权频率函数构建，而消失阶结果则由相关但不同的加权频率函数推导得出。
英文摘要
We study quantitative unique continuation for bi-Laplace equations \[Δ^{2}u+V(x)u=0 \] by introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and Hölder 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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