数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 58-68.doi: 10.1016/S0252-9602(16)30115-1

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GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL

向长林   

  1. Department of Mathematics and Statistics, University of Jyvaskyla, P. O. Box 35, FI-40014 University of Jyvaskyla, Finland
  • 收稿日期:2015-11-30 出版日期:2017-02-25 发布日期:2017-02-25
  • 作者简介:Changlin XIANG,E-mail:changlin.c.xiang@jyu.fi
  • 基金资助:

    The author is financially supported by the Academy of Finland, project 259224.

GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL

Changlin XIANG   

  1. Department of Mathematics and Statistics, University of Jyvaskyla, P. O. Box 35, FI-40014 University of Jyvaskyla, Finland
  • Received:2015-11-30 Online:2017-02-25 Published:2017-02-25
  • About author:Changlin XIANG,E-mail:changlin.c.xiang@jyu.fi
  • Supported by:

    The author is financially supported by the Academy of Finland, project 259224.

摘要:

This note is a continuation of the work[17]. We study the following quasilinear elliptic equations
-△pu-(μ)/(|x|p)|u|p-2u=Q(x)|u|(Np)/(N-p)-2u, x∈RN,
where 1 < p < N, 0≤μ < ((N-p)/p)p and QL(RN). Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

关键词: quasilinear elliptic equations, Hardy's inequality, gradient estimate

Abstract:

This note is a continuation of the work[17]. We study the following quasilinear elliptic equations
-△pu-(μ)/(|x|p)|u|p-2u=Q(x)|u|(Np)/(N-p)-2u, x∈RN,
where 1 < p < N, 0≤μ < ((N-p)/p)p and QL(RN). Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

Key words: quasilinear elliptic equations, Hardy's inequality, gradient estimate