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# Cases a) and b)

Source publication
Research Proposal
Full-text available
Recently translated father's 1968 Ph.D. Thesis, appears to be related to Hilbert's Problem #21, in the context of Theory of Elasticity using Complex Variables. The Hilbert kernel is stressed on various points and a complete solution for its elastic profile is given up to compromise. The crack is described using analytic functions.

## Contexts in source publication

Context 1
... z is a real variable such that 0 ≤ |z| ≤ R and ds = −dz because of cos(n, x) = 0 and cos(n, y) = 1. The components X n , Y n are found as follows for the three basic cases of charge: a) For continuous, uniformly distributed, normal charge on a section of the contour (Fig. ...
Context 2
... For continuous, uniformly distributed, tangential charge q on a section of the contour (Fig. 7b). X n = q, Y n = 0 for z between z ′ z ′′ . c) For given stresses σ ∞ x , σ ∞ y and τ ∞ xy where X n = Y n = 0. 4. Examining the structure of the functions Φ ′ 1 (z 1 ), Φ ′ 2 (z 2 ) in equations (17) we ...

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