Boundary values and the transformation problem for constant principal strain mappings

Julian Gevirtz

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-38

Abstract:

We initiate a study of homeomorphisms f with constant principal strains (cps) between smoothly bounded planar domains D , D ′ . An initial result shows that in order for there to be such a mapping of a given Jordan domain D onto D ′ , a certain condition of an isoperimetric nature must be satisfied by the latter. Thereafter, we establish the fundamental fact that principal strain lines (characteristics) of such mappings necessarily have well-defined tangents where they meet ∂ D . Using this, we obtain information about the boundary values of the Jacobian transformation of f , and finally we determine the class of all cps-homeomorphisms of a half-plane onto itself.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:657924

DOI: 10.1155/S0161171203204166

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