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Non-Archimedean Neumann problem: weak and strong solutions

Published 28 Aug 2025 in math.AP and math.NT | (2508.20548v1)

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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