1.

Bandle, C., *Isoperimetric Inequalities and their Applications*. Pitman, Essex, 1980.

2.

Breuer, S. & Roseman, J. J., Phragmén-Lindelöf decay theorems for classes of nonlinear Dirichlet problems in a circular cylinder. *J. Math. Anal. Appl.*
**113**, 59–77 (1986).

3.

Carslaw, H. S. & Jaeger, J. C., *Conduction of Heat in Solids* (Second Edition). Oxford University Press, Oxford, 1959.

4.

Flavin, J. N., Knops, R. J. & Payne, L. E., Asymptotic behavior of solutions of semi-linear elliptic equations on the half-cylinder *Z. Angew. Math. Phys.*
**43**, 405–421 (1992).

5.

Fu, S. & Wheeler, L. T., Stress bounds for bars in torsion. *J. Elasticity*
**3**, 1–13 (1973).

6.

Horgan, C. O., Recent developments concerning Saint-Venant's principle: an update. *Applied Mechanics Reviews*
**42**, 295–303 (1989).

7.

Horgan, C. O. & Knowles, J. K., Recent developments concerning Saint-Venant's principle. *Advances in Applied Mechanics*, J. W. Hutchinson, ed., Vol. 23, pp. 179–269. Academic Press, New York, 1983.

8.

Horgan, C. O. & Olmstead, W. E., Exponential decay estimates for a class of nonlinear Dirichlet problems. *Arch. Rational Mech. Anal.*
**71**, 221–235 (1979).

9.

Horgan, C. O. & Payne, L. E., Lower bounds for free membrane and related eigenvalues. *Rendiconti di Matematica*, Serie VII, **10**, 457–491 (1990).

10.

Horgan, C. O. & Payne, L. E., Decay estimates for a class of nonlinear boundary value problems. *SIAM J. Math. Anal.*
**20**, 782–788 (1989).

11.

Horgan, C. O. & Payne, L. E., A Saint-Venant principle for a theory of nonlinear plane elasticity. *Q. Appl. Math.*
**50**, 641–645 (1992).

12.

Horgan, C. O., Payne, L. E. & Simmonds, J. G., Existence, uniqueness and decay estimates for solutions in the nonlinear theory of elastic, edge-loaded, circular tubes. *Quart. Appl. Math.*
**48**, 341–359 (1990).

13.

Knops, R. J. & Payne, L. E., A Phragmén-Lindelöf principle for the equation of a surface of constant mean curvature (to appear).

14.

Payne, L. E., Isoperimetric inequalities and their applications. *SIAM Review*
**9**, 453–488 (1967).

15.

Payne, L. E., Bounds for the maximum stress in the St.-Venant torsion problem. *Indian J. Mech. Math.* (Special issue dedicated to B. Sen) 51–59 (1968).

16.

Payne, L. E., Some comments on the past fifty years of isoperimetric inequalities, in *Inequalities: Fifty Years on from Hardy, Littlewood and Pólya*, W. N. Everitt, ed., pp. 143–161, Marcel Dekker, New York, 1991.

17.

Payne, L. E.. & Philippin, G. A., Isoperimetric inequalities in the torsion and clamped membrane problems for convex plane domains. *SIAM J. Math. Anal.*
**14**, 1154–1162 (1983).

18.

Payne, L. E.. & Weinberger, H. R., An optimal Poincaré inequality for convex domains. *Arch. Rational Mech. Anal.*
**5**, 182–188 (1960).

19.

Sperb, R. P., *Maximum Principles and their Applications*. Academic Press, New York, 1981.

20.

Vafeades, P.. & Horgan, C. O., Exponential decay estimates for solutions of the von Kármán equations on a semi-infinite strip. *Arch. Rational Mech. Anal.*
**104**, 1–25 (1988).