Classification of extremal functions to logarithmic Hardy-Littlewood-Sobolev inequality on the upper half space

DOI10.3934/DCDS.2018171zbMath1404.35006OpenAlexW2806802807WikidataQ129697511 ScholiaQ129697511MaRDI QIDQ1661147

Ye Li, Jingbo Dou

Publication date: 16 August 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018171

zbMATH Keywords

extremal functionsKelvin transformationmethod of moving spheres

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Systems of nonlinear integral equations (45G15) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

Fractional equations with indefinite nonlinearities ⋮ Direct methods on fractional equations ⋮ Liouville's theorem for a fractional elliptic system

Cites Work

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• Sharp Reversed Hardy–Littlewood–Sobolev Inequality on the Half Space $\mathbf{R}_+^n$
• Sharp Hardy–Littlewood–Sobolev Inequality on the Upper Half Space

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