The Vladimirov-Taibleson operator: inequalities, Dirichlet problem, boundary Holder regularity

被引：1

作者：

Kochubei, Anatoly N. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, Tereshchenkivska 3, UA-01024 Kiev, Ukraine

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2023年 / 14卷 / 02期

关键词：

Fractional differentiation operator; Non-Archimedean local field; Riesz potentials; Dirichlet problem; Boundary regularity; SOBOLEV SPACES; EXISTENCE; EQUATIONS;

D O I：

10.1007/s11868-023-00525-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Holder regularity of solutions.

引用

页数：27

共 9 条

[1] The Vladimirov–Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity
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Journal of Pseudo-Differential Operators and Applications, 2023, 14
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