Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 119, Issue -, Pages 179-185Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2014.09.009
Keywords
Sobolev-Hardy inequality; Minimizer; Radial symmetry; Decaying law
Categories
Funding
- NNSF of China [11271170]
- GAN PO 555 program of Jiangxi
- NNSF of Jiangxi [2012BAB201008]
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In this paper, we show that the minimizing problem Lambda(s,alpha) = inf(u(H) over dots(RN), u not equivalent to 0) integral(RN)vertical bar-Delta(s/2)u(x)vertical bar(2) dx/(integral(RN)vertical bar u(x)vertical bar(2)*(s,alpha)/vertical bar x vertical bar(alpha) dx)(2/2)*(s,alpha) (1) is achieved by a positive, radially symmetric and strictly decreasing function provided 0 < s < N/2, 0 < alpha < 2s. (C) 2014 Elsevier Ltd. All rights reserved.
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