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<p>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.</p>

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Non-Archimedean Neumann problem: weak and strong solutions

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Alexandra V. Antoniouk,
  • Anatoly N. Kochubei

摘要

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.