Regularity lifting result for an integral system involving Riesz potentials
| dc.contributor.author | Li, Yayun | |
| dc.contributor.author | Xu, Deyun | |
| dc.date.accessioned | 2022-09-08T16:32:58Z | |
| dc.date.available | 2022-09-08T16:32:58Z | |
| dc.date.issued | 2017-11-14 | |
| dc.description.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]. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Li, Y., & Xu, D. (2017). Regularity lifting result for an integral system involving Riesz potentials. Electronic Journal of Differential Equations, 2017(284), pp. 1-8. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16129 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Riesz potential | |
| dc.subject | Integral system | |
| dc.subject | Regularity lifting lemma | |
| dc.subject | Hartree equation | |
| dc.subject | Hardy-Littlewood-Sobolev inequality | |
| dc.title | Regularity lifting result for an integral system involving Riesz potentials | |
| dc.type | Article |