Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-30T06:18:40.162Z Has data issue: false hasContentIssue false
  • English
  • Français

An Axisymmetric Boundary Value Problem of Mixed Type for a Half-space

Published online by Cambridge University Press:  20 January 2009

M. Lowengrub  and
I. N. Sneddon
M. Lowengrub
Affiliation:
North Carolina State College, Raleigh, North Carolina
I. N. Sneddon
Affiliation:
The University, Glasgow
Rights & Permissions [Opens in a new window]

Extract

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.

In problems in the mathematical theory of elasticity related to the symmetric deformation of an infinite elastic solid with an external crack we encounter the problem of determining an axisymmetric function φ(ρ, z) which is harmonic in the half-space z>0 and satisfies the mixed boundary conditions

on the plane boundary z = 0, where it is assumed that f(ρ) is continuously differentiable in [1, ∞). Further φ→0 as √(ρ2+z2)→∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 39 - 46
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Williams, W. E., The solution of certain dual integral equations, Proc. Edin-burgh Math. Soc., 12 (Ser. ii) (1961), 213.CrossRefGoogle Scholar
(2) Sneddon, I. N., The elementary solution of dual integral equations, Proc. Glasgow Math. Assoc., 4 (1960), 108.CrossRefGoogle Scholar
(3) Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd edn. (Univ-ersity Press, Cambridge, 1944).Google Scholar
(4) Green, A. E. and Zerna, W., Theoretical Elasticity (Clarendon Press, Oxford, 1954).Google Scholar
(5) Pearson, K., Editor, Tables of the Incomplete Beta Function (University Press, Cambridge, 1932).Google Scholar