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关于一类向量场的Picone恒等式和Hardy不等式 被引量:9

PICONE IDENTITY AND HARDY INEQUALITY FOR A CLASS OF VECTOR FIELDS
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摘要 本文给出了构成Baouendi-Grushin算子 的向量场的Picone恒 式,由此导出了Hardy不等式.已有文献中得到的不等式成为本文结果的特殊情形。 In this paper, the Picone identity and Hardy inequality for a dais of vector fields which construct the Baouendi-Grushin operator are given and the known result in a reference u a particular case here.
出处 《数学杂志》 CSCD 北大核心 2003年第1期121-125,共5页 Journal of Mathematics
基金 国家自然科学基金资助项目(99C12)
关键词 PICONE恒等式 HARDY不等式 向量场 Picone identity, Hardy inequality, vector field.
  • 相关文献

参考文献3

  • 1Hardy, G.H., Littlewood, J.E. and Polya, G. Inequalities,[M]. Cambrideg Univ. Press, 2nded. 1952.
  • 2Allegretto, W. and Huang, Y.X., A Picone's identity for the p-Laplacian and application. [J]. Nonlinear Aualysis, 1998. 32(7): 819-830.
  • 3Garofalo, N.,Unique Continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension[J]. J.Diff. Equ. 1993,(104): 117-146.

同被引文献62

  • 1窦井波,韩亚洲.广义Baouendi-Grushin向量场上抛物型不等方程弱解的不存在性[J].郑州大学学报(理学版),2005,37(4):1-8. 被引量:2
  • 2BAOUENDI M S.Sur une classe d'operateurs elliptiques degeneres[J].Bull Soc Math France,1967,95:45-87.
  • 3GRUSIN V V.On a class of hypoelliptie operators[J].Math USSR Sbornik,1970,12(3):458-476.
  • 4GAROFALO N.Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension[J].J Differential Equations,1993,104 (1):117-146.
  • 5GAROFALS N,NHIE D M.Isoperimetric and Sobolev inequalities for Carnot-Caratheodory spaces and the existence of minimum surfaces[J].Comm Pure Appl Math,1996,49 (10):1081-1144.
  • 6GARCIA A J,PERAL I.Hardy inequality and some critical elliptic and parabolic problems[J].J Diff Eqs,1998,144 (2):441-476.
  • 7D'AMBROZIO L.Some Hardy inequalities on the Heisenberg group[J].Differential Equations,2004,40 (4):552-564.
  • 8MONTI R,MORBIDELLI D.Kelvin transform for Grushin operators and critical semilinear equations[J].Duke Math J,2006,131 (1):167-202.
  • 9NIU Peng-cheng,DOU Jing-bo.Hardy-Sobolev type inequalities for generalized Baouendi-Grushin operators[J].Miskolc Mathematical Notes,2007,8(1):73-87.
  • 10D'Ambrosio L.Hardy Inequlities related to Grushin type operators[J]. Proc Amer Math Soc,2003,132(3):725.

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