Regularity lifting result for an integral system involving Riesz potentials
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Date
2017-11-14
Authors
Li, Yayun
Xu, Deyun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the integral system involving the Riesz potentials
u(x) = √p ∫ℝn up-1(y)v(y)dy/|x-y|n-α, u > 0 in ℝn,
v(x) = √p ∫ℝn up(y)dy/|x-y|n-α v > 0 in ℝn,
where n ≥ 1, 0 < α < n and p > 1. Such a system is related to the study of a static Hartree equation and the Hardy-Littlewood-Sobolev inequality. We investigate the regularity of positive solutions and prove that some integrable solutions belong to C1(ℝn). An essential regularity lifting lemma comes into play, which was established by Chen, Li and Ma [20].
Description
Keywords
Riesz potential, Integral system, Regularity lifting lemma, Hartree equation, Hardy-Littlewood-Sobolev inequality
Citation
Li, Y., & Xu, D. (2017). Regularity lifting result for an integral system involving Riesz potentials. <i>Electronic Journal of Differential Equations, 2017</i>(284), pp. 1-8.
Rights
Attribution 4.0 International