The minimizing problem involving $p$-Laplacian and Hardy–Littlewood–Sobolev upper critical exponent

In this paper, we study the minimizing problem $$ S_{p,1,\alpha,\mu}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - \mu \int_{\mathbb{R}^{N}} \frac{|u|^{p}}{|x|^{p}} \mathrm{d}x} {\left( \int_{\mathbb{R}^{N}} \int_{\mathbb{R}^{N}} \frac{|u...

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Bibliographic Details

Published in:	Electronic Journal of Qualitative Theory of Differential Equations
Main Authors:	Yu Su, Haibo Chen
Format:	Article
Language:	English
Published:	University of Szeged 2018-08-01
Subjects:	refinement of hardy–littlewood–sobolev inequality hardy–littlewood–sobolev upper critical exponent $p$-laplacian minimizing
Online Access:	http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6753