Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - Volume 13 - Issue01

Research Article

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

M. Lowengruba1 and I. N. Sneddona2†

a1 North Carolina State College, Raleigh, North Carolina

a2 The University, Glasgow

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

S0013091500014474_eqn1

S0013091500014474_eqn2

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

(Received October 02 1961)

Footnotes

† The work described in this paper was done in the Department of Mathematics' Duke University, North Carolina, and was supported in part by the U.S. Air Force Office of Scientific Research, A.R.D.C., under contract AF 18(600)-1341

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