ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES

Authors

  • B. G. PACHPATTE Department of Mathematics and Statistics, Marathwada University, Aurangabad 431004, (Maharashtra), INDIA.

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4587

Keywords:

Sobolev inequality, Lieb inequality, Thirring inequality, discrete inequalities, scalar functions of many variables

Abstract

Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities.

References

J. A. Dubinskii', "Some integral inequalities and the solvability of degenerate quasilinear elliptic systems of differential equations," Math. Sb. 64 (1964), 458-480.

A. Friedman, "Partial Differential Equations", New York:Holt, Reinhart and Winston, 1969.

J. M. Ghidaglia, M. Marion and R. Temam, "Generalization of the Sobolev-Licb-Thirring inequalities and applications to the dimension of attractors," Differential and Integral Equations 1 (1988), 1-21.

E. Lieb and W. Thirring, Inequalities for the moments of the eigenvalues of the Schrodinger Hamiltonian and their relation to Sobolev inequalities, in Studies in Mathematical Physics, E. Lieb, B. Simon and A.Wightman Eds.Princeton Univ.P1·css, Princeton, 1976.

B. G. Pachpattc, "On Sobolev type inequalities," Proc. Royal Soc. Edinburgh 103A (1986), 1-14.

B. G. Pachpatte, On discrete inequalities of the Poincare type, Periodica Math. Hungarica 19 (1988), 227-233.

B. G. Pachpatte, "On some new multidimensi~nal discrete inequalities," Tamkang Jour. Math. 17 (1986), 21-29.

P. M. Prenter, "Splines and Variational Methods", Wiley, New York, 1975.

Downloads

Published

1991-06-01

How to Cite

PACHPATTE, B. G. (1991). ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES. Tamkang Journal of Mathematics, 22(2), 145–151. https://doi.org/10.5556/j.tkjm.22.1991.4587

Issue

Section

Papers