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Advanced Nonlinear Studies

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Volume 16, Issue 3


Weighted Fractional Sobolev Inequality in ℝN

Xiaoli Chen / Jianfu Yang
  • Corresponding author
  • Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China
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Published Online: 2016-03-12 | DOI: https://doi.org/10.1515/ans-2015-5002


In this paper, we show that the minimizing problem


is achieved by a positive, cylindrically symmetric and strictly decreasing function u(x) provided 0<s<N2, 0<α<2s, where x=(y,z)k×N-k and 2s,α*=2(N-α)N-2s. Decaying laws for the minimizer u are also established.

Keywords: Sobolev–Hardy Inequality; Minimizer; Cylindrical Symmetry; Decaying Law

MSC 2010: 35A15; 35J20; 35J61; 36J75


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About the article

Received: 2015-05-27

Revised: 2015-09-20

Accepted: 2015-09-27

Published Online: 2016-03-12

Published in Print: 2016-08-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11461033

Award identifier / Grant number: 11401269

Award identifier / Grant number: 11271170

Award identifier / Grant number: 11361029

X. Chen is supported by the NNSF of China (no. 11461033 and 11401269) and the NNSF of Jangxi Province (no. 20142BAB201003). J. Yang is supported by the NNSF of China (no. 11271170 and 11361029) and the GAN PO 555 program of Jiangxi.

Citation Information: Advanced Nonlinear Studies, Volume 16, Issue 3, Pages 623–641, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2015-5002.

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