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The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary H\"older Regularity
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Abstract
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 H\"older regularity of solutions.
MSC 2020. Primary: 35S05. Secondary: 11S80, 47G30, 35S11; 35R11.
Title: The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary H\"older Regularity
Description:
Abstract
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 H\"older regularity of solutions.
MSC 2020.
Primary: 35S05.
Secondary: 11S80, 47G30, 35S11; 35R11.
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