arXiv:2209.07998 Abstract | arXiv Analytics

arXiv:2209.07998 [math.AP]Abstract References Reviews Resources

The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity

Published 2022-09-16Version 1

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.

Categories: math.AP, math.FA, math.NT

Subjects: 35S05, 11S80, 47G30, 35S11, 35R11

Keywords: boundary hölder regularity, vladimirov-taibleson operator, dirichlet problem, inequalities, non-archimedean local field

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