PreprintCC BY 4.0HAL
Neumann Boundary Value Problems on p-Adic Analytic Manifolds
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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BibTeX
@misc{bradley2026neumann,
title = {{Neumann Boundary Value Problems on p-Adic Analytic Manifolds}},
author = {Patrick Erik Bradley},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26180},
eprint = {2609.26180},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05749511v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Neumann Boundary Value Problems on p-Adic Analytic Manifolds
AU - Patrick Erik Bradley
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.26180
UR - https://hal.science/hal-05749511v1
AB - 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.
ER -