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# Intersection of planes z 1 , z 2 and ζ 1 , ζ 2

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Research Proposal
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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.

## Context in source publication

Context 1
... coincidence of the points z, z 1 and z 2 on the boundary C implies the same for ζ, ζ 1 and ζ 2 on the unit circles (and conversely), a conclusion which allows us to refer to one unit circle(c) the one found on the "intersection" of the planes ζ 1 and ζ 2 (Fig. 8). In order for transformation (21) to be invertible it must have a non-vanishing first derivative therefore it must have ζ 2 i − 1 ̸ = 0 or ζ i ̸ = ±1, a result which was expected because of the existence of a cusp 16 in the above positions. The transformations (21) substituted into relations (17) ...

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