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  • Bulletin of the Australian Mathematical Society, Volume 63, Issue 2
  • April 2001, pp. 321-327

Some New Poincaré-type inequalities

  • Wing-Sum Cheung (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700019365
  • Published online: 01 April 2009
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]E.F. Beckenbach and R. Bellman , Inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1965).

[2]W.S. Cheung , ‘On integral inequalities of the Sobolev type’, Aequationes Math. 49 (1995), 153159.

[3]W.S. Cheung , ‘On Poincaré-type integral inequalities’, Proc. Amer. Math. Soc. 119 (1993), 857863.

[8]C.O. Horgan , ‘Integral bounds for solutions of nonlinear reaction-diffusion equations’, Z. Angew. Math. Phys. 28 (1977), 197204.

[9]C.O. Horgan and R.R. Nachlinger , ‘On the domain of attraction for steady states in heat conduction’, Internat. J. Engrg. Sci. 14 (1976), 143148.

[10]C.O. Horgan and L.T. Wheeler , ‘Spatial decay estimates for the Navier-Stokes equations with applications to the problem of entry flow’, SIAM J. Appl. Math. 35 (1978), 97116.

[11]G.V. Milovanović , D.S. Mitrinović and Th.M. Rassias , Topics in polynomials: Extremal problems inequalities, zeros (World Scientific Publishing Co., River Edge, N.J., 1994).

[12]D.S. Mitrinović , Analytic inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1970).

[14]B.G. Pachpatte , ‘On Poincaré type integral inequalities’, J. Math. Anal. Appl. 114 (1986), 111115.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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