On fractional harmonic functions
Huyuan Chen, Ying Wang
TL;DR
This paper investigates the properties of fractional harmonic functions, classifying polynomials and analyzing boundary singularities, advancing understanding of fractional Laplacian-related harmonic functions.
Contribution
It provides a classification of polynomials for the fractional Laplacian and studies boundary singularities of fractional harmonic functions.
Findings
Classified polynomials in whole and half spaces for fractional Laplacian.
Analyzed fractional harmonic functions with boundary singularities.
Derived distributional identities related to these functions.
Abstract
Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined in a principle value sense at infinity. Secondly, we study the fractional harmonic functions in half space with singularities on the boundary and the related distributional identities.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Numerical methods in inverse problems