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arXiv · 2609.26180

Neumann Boundary Value Problems on $p$-Adic Analytic Manifolds

Patrick Erik Bradley
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Abstract

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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Patrick Erik Bradley. 2026-08-09. Neumann Boundary Value Problems on $p$-Adic Analytic Manifolds. https://arxiv.org/abs/2609.26180

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