On fractional harmonic functions

Huyuan Chen; Ying Wang

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arXiv · 2203.10312

On fractional harmonic functions

Huyuan Chen·Ying Wang

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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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Huyuan Chen, Ying Wang. 2022-03-19. On fractional harmonic functions. https://arxiv.org/abs/2203.10312

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