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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 12, Pages 739-776
http://dx.doi.org/10.1155/S0161171203204166

Boundary values and the transformation problem for constant principal strain mappings

1Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile and Academia Chilena de Ciencias, Almirante Montt 454, Santiago, Chile
22005 North Winthrop Road, Muncie, IN 47304, USA

Received 17 April 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.