AI 中文总结
本文受图论启发，在 $p$-adic 解析流形上提出 Neumann 边值问题，证明超压缩情形下弱解存在唯一性，并利用该问题检测解析函数零点。
AI 中文摘要
受图论启发，在 $p$-adic 解析流形上提出了 Neumann 边值问题。在超压缩情形下证明了弱解的存在唯一性。为此，证明了 $p$-adic Gauss-Green 恒等式以及流形上具有小支撑的小波的扩展特征值公式。作为应用，证明了流形上解析函数接近零点可通过 Neumann 边值问题检测。
英文摘要
Inspired by graph theory, Neumann Boundary Value Problems on $p$-adic analytic manifold are formulated. Existence and uniqueness of weak solutions is proven in the ultracontractive case. For this task, a $p$-adic Gauss-Green identity and an extended eigenvalue formula for wavelets with small supports on the manifold are proven. As an application, the closeness to a zero of an analytic function on the manifold is shown to be detectable via a Neumann Boundary Value Problem.
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