The Vladimirov–Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity

We study the Vladimirov–Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field. We prove analogs of classical inequalities for fractional Laplacian, study the counterpart of the Dirichlet problem incl...

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Bibliographic Details
Published in:Journal of pseudo-differential operators and applications 2023-06, Vol.14 (2), Article 31
Main Author: Kochubei, Anatoly N.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Differential equations
Dirichlet problem
Functional Analysis
Inequalities
Mathematics
Mathematics and Statistics
Operator Theory
Operators (mathematics)
Partial Differential Equations
Regularity
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Summary:We study the Vladimirov–Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field. We prove analogs of classical inequalities for fractional Laplacian, study the counterpart of the Dirichlet problem including the property of boundary Hölder regularity of solutions.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-023-00525-7