Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On Poincaré type integral inequalities


Author: Wing Sum Cheung
Journal: Proc. Amer. Math. Soc. 119 (1993), 857-863
MSC: Primary 26D10
DOI: https://doi.org/10.1090/S0002-9939-1993-1169023-8
MathSciNet review: 1169023
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper some new integral inequalities of the Poincaré type, on a region of rectangular dimensions, involving many functions in many variables are obtained. These in turn can be used to serve as generators of other integral inequalities.


References [Enhancements On Off] (What's this?)

  • [1] E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, New York, 1965. MR 0192009 (33:236)
  • [2] W. S. Cheung, Some new Opial-type inequalities, Mathematika 37 (1990), 136-142. MR 1067894 (91j:26017)
  • [3] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1952. MR 0046395 (13:727e)
  • [4] C. O. Horgan, Integral bounds for solutions of nonlinear reaction-diffusion equations, J. Appl. Math. Phys. (ZAMP) 28 (1977), 197-204. MR 0442481 (56:863)
  • [5] C. O. Horgan and R. R. Nachlinger, On the domain of attraction for steady states in heat conduction, Internat. J. Engrg. Sci. 14 (1976), 143-148. MR 0449203 (56:7508)
  • [6] 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), 97-116. MR 0502782 (58:19708)
  • [7] D. S. Mitrinović, Analytic inequalities, Springer-Verlag, Berlin, 1970. MR 0274686 (43:448)
  • [8] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1959), 116-162. MR 0109940 (22:823)
  • [9] B. G. Pachpatte, On Poincaré-type integral inequalities, J. Math. Anal. Appl. 114 (1986), 111-115. MR 829115 (87d:26018)
  • [10] -, On some new integral inequalities in several independent variables, Chinese J. Math. 14 (1986), 69-79. MR 857161 (87i:26023)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26D10

Retrieve articles in all journals with MSC: 26D10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1169023-8
Keywords: Poincaré inequality
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society