Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T03:05:32.560Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on a class of integral inequalities

Published online by Cambridge University Press:  24 October 2008

Cornelius O. Horgan
Cornelius O. Horgan
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NOR 88C, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A unified variational approach to a class of second-order integral in-equalities is presented. A special case recently considered in a different manner by Anderson, Arthurs and Hall (1) is recovered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 127 - 131
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Anderson, N., Arthurs, A. M. and Hall, R. R.Extremum principle for a nonlinear problem in magneto-elasticity. Proc. Cambridge Philos. Soc. 72 (1972), 315–31CrossRefGoogle Scholar
(2)Courant, R. and Hilbert, D.Methods of mathematical physics, vol. 1 (Interscience, New York, 1953).Google Scholar
(3)Mikhlin, S. G.The problem of the minimum of a quadratic functional (Holden-Day, San Franscico, 1965).Google Scholar
(4)Young, D. Continuous systems. Chapter 61 of Handbook of engineering mechanics, edited by FlÜgge, W. (McGraw-Hill, New York, 1962).Google Scholar
(5)PÓlya, G. and Szecö, G.Isoperimetric inequalities in mathematical physics. Annals of Mathematics Studies, No. 27 (Princeton University Press, Princeton, 1951).Google Scholar
(6)Hardy, G. H., Littlewood, J. E. and Pólya, G.Inequalities. Second edition (Cambridge, 1952).Google Scholar
(7)Beckenbach, E. F. and Bellman, R.Inequalities. Third Printing (Springer-Verlag, Berlin, 1971).Google Scholar
(8)Mitrinovíc, D. S.Analytic inequalities (Springer-Verlag, Berlin, 1970).CrossRefGoogle Scholar
(9)Fan, K., Taussky, O. and Todd, J.Discrete analogues of inequalities of Wirtinger. Monatschefte für Mathematik, 59 (1955), 73–90.CrossRefGoogle Scholar
(10)Beesack, P. R.Integral inequalities of the Wirtinger type. Duke Math. J. 25 (1958), 477–498.CrossRefGoogle Scholar
(11)Benson, D. C.Inequalities involving integrals of functions and their derivatives. J. Math. Anal. Appl. 17 (1967), 292–308.CrossRefGoogle Scholar