On super polyharmonic property of high-order fractional Laplacian

2022/03/19 by Xu, Meiqing
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.10208

Abstract

Let 0 0 for k=1,...m under different conditions (-Δ)^mu\inL_α and (-Δ)^m u≥ 0. Both kinds of super polyharmonic properties can lead to the equivalence between the PDE and the integral equation u(x)=∫_ℝⁿ\fracu^p(y)|x-y|^n-2m-αdy.

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