# Non-Archimedean Neumann problem: weak and strong solutions

## TL;DR

This paper investigates the Neumann problem involving the Vladimirov-Taibleson fractional operator over non-Archimedean fields, analyzing weak and strong solutions using ultrametric identities and extending previous methods.

## Contribution

It introduces a framework for studying weak and strong solutions of the Neumann problem in non-Archimedean analysis, utilizing ultrametric identities for the fractional operator.

## Key findings

- Established existence of weak solutions using adapted methods.
- Derived conditions for strong solutions based on ultrametric identities.
- Extended classical Neumann problem analysis to non-Archimedean settings.

## Abstract

We consider the Neumann problem for the equation with the Vladimirov-Taibleson fractional differentiation operator over a non-Archimedean local field. We study weak solutions following the method by Dipierro, Ros-Oton and Valdinoci (2017). Our investigation of strong solutions is based on the ultrametric identities for the operator under consideration.