The optimal constant in Hardy-type inequalities

To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite in...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 31; no. 5; pp. 731 - 754
Main Author Chen, Mu-Fa
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2015
Springer Nature B.V
Subjects
Approximation
Constants
Estimates
Eulers equations
Inequalities
Inequality
Intervals
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Studies
Theorems
optimal constant
26D10
60J60
approximating procedure
34L15
Hardy-type inequality
variational formulas
Online AccessGet full text
ISSN1439-8516
1439-7617
DOI10.1007/s10114-015-4731-5

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Summary:To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4731-5