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A note on a class of integral inequalities

Published online by Cambridge University Press:  24 October 2008

Cornelius O. Horgan
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NOR 88C, U.K.

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
Copyright
Copyright © Cambridge Philosophical Society 1973

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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), 7390.CrossRefGoogle Scholar
(10)Beesack, P. R.Integral inequalities of the Wirtinger type. Duke Math. J. 25 (1958), 477498.CrossRefGoogle Scholar
(11)Benson, D. C.Inequalities involving integrals of functions and their derivatives. J. Math. Anal. Appl. 17 (1967), 292308.CrossRefGoogle Scholar