Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T10:39:01.974Z Has data issue: false hasContentIssue false

Some New Poincaré-type inequalities

Published online by Cambridge University Press:  17 April 2009

Wing-Sum Cheung
Affiliation:
Department of Mathematics, The University of Hong Kong, Hong Kong, e-mail: wscheung@hkucc.hku.hk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

New and improved Poincaré-type integral inequalities involving many functions of many variables are established. These in turn can serve as generators and can generate numerous Poincaré-type integral inequalities by choosing different parameters.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Beckenbach, E.F. and Bellman, R., Inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1965).CrossRefGoogle Scholar
[2]Cheung, W.S., ‘On integral inequalities of the Sobolev type’, Aequationes Math. 49 (1995), 153159.CrossRefGoogle Scholar
[3]Cheung, W.S., ‘On Poincaré-type integral inequalities’, Proc. Amer. Math. Soc. 119 (1993), 857863.Google Scholar
[4]Cheung, W.S., ‘Some multi-dimensional integral inequalities’, in Nonlinear Mathematical Analysis and its Applications, (Rassias, Th.M., Editor) (Hadronic Press, Palm Harbor, 1998), pp. 1938.Google Scholar
[5]Cheung, W.S., ‘Some new Opial-type inequalities’, Mathematika 37 (1990), 136142.CrossRefGoogle Scholar
[6]Cheung, W.S., Hanjš, Z. and Pečarić, J., ‘On Wirtinger-type integral inequalities’, (preprint).Google Scholar
[7]Hardy, G.H., Littlewood, J.E. and Pólya, G., Inequalities (Cambridge Univ. Press, Cambridge, 1952).Google Scholar
[8]Horgan, C.O., ‘Integral bounds for solutions of nonlinear reaction-diffusion equations’, Z. Angew. Math. Phys. 28 (1977), 197204.CrossRefGoogle Scholar
[9]Horgan, C.O. and Nachlinger, R.R., ‘On the domain of attraction for steady states in heat conduction’, Internat. J. Engrg. Sci. 14 (1976), 143148.CrossRefGoogle Scholar
[10]Horgan, C.O. and Wheeler, L.T., ‘Spatial decay estimates for the Navier-Stokes equations with applications to the problem of entry flow’, SIAM J. Appl. Math. 35 (1978), 97116.CrossRefGoogle Scholar
[11]Milovanović, G.V., Mitrinović, D.S. and Rassias, Th.M., Topics in polynomials: Extremal problems inequalities, zeros (World Scientific Publishing Co., River Edge, N.J., 1994).CrossRefGoogle Scholar
[12]Mitrinović, D.S., Analytic inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1970).CrossRefGoogle Scholar
[13]Nirenberg, L., ‘On elliptic partial differential equations’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1959), 116162.Google Scholar
[14]Pachpatte, B.G., ‘On Poincaré type integral inequalities’, J. Math. Anal. Appl. 114 (1986), 111115.CrossRefGoogle Scholar
[15]Pachpatte, B.G., ‘On some new integral inequalities in several independent variables’, Chinese J. Math. 14 (1986), 6979.Google Scholar
[16]Rassias, Th.M., ‘On certain properties of eigenvalues and the Poincaré inequality’, in Global Analysis - Analysis on Manifolds, Teubner-Texte zur Math 57 (Teubner, Leipzig, 1983), pp. 282300.Google Scholar
[17]Rassias, Th.M., ‘Un contre-exemple à l'inégalité de Poincaré’, C. R. Acad. Sciences Paris 284 (1977), 409412.Google Scholar