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arXiv · 2508.20548

Non-Archimedean Neumann problem: weak and strong solutions

Alexandra V. Antoniouk·Anatoly N. Kochubei
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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.

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Alexandra V. Antoniouk, Anatoly N. Kochubei. 2025-08-28. Non-Archimedean Neumann problem: weak and strong solutions. https://arxiv.org/abs/2508.20548

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