Non-Archimedean Neumann problem: weak and strong solutions

2025/08/28 by Alexandra V. Antoniouk, Antoniouk, Alexandra V., Anatoly N. Kochubei +1
Mathematics · #11S80 #35S15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2508.20548

openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Existence and uniqueness for p-adic counterpart of the porous medium equation
• The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity
• The Wiener--Hopf Technique, its Generalisations and Applications: Constructive and Approximate Methods
• L^p properties of non-Archimedean fractional differentiation operators
• Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables
• Linear and Nonlinear Heat Equations on a p-Adic Ball
• p-Adic Analogue of the Porous Medium Equation
• Nonlocal problems with Neumann boundary conditions
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces

Related

• L^p properties of non-Archimedean fractional differentiation operators
• The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity
• Nonlocal operators with Neumann conditions
• Nonlinear Pseudo-Differential Equations for Radial Real Functions on a Non-Archimedean Field
• Existence of nonnegative solutions for fractional Schrödinger equations with Neumann condition