Non-Archimedean Neumann problem: weak and strong solutions
Analysis of PDEs
2025-08-29 v1 Number Theory
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.
Cite
@article{arxiv.2508.20548,
title = {Non-Archimedean Neumann problem: weak and strong solutions},
author = {Alexandra V. Antoniouk and Anatoly N. Kochubei},
journal= {arXiv preprint arXiv:2508.20548},
year = {2025}
}