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International Journal of Mathematics and Mathematical Sciences - Volume 2003 2003, Issue 12, Pages 739-776



Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile and Academia Chilena de Ciencias, Almirante Montt 454, Santiago, Chile

2005 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 principalstrains cps between smoothly bounded planar domains D, D′. An initial result shows that in orderfor there to be such a mapping of a given Jordan domain D ontoD′, a certain condition of an isoperimetric nature must besatisfied by the latter. Thereafter, we establish the fundamentalfact that principal strain lines characteristics of suchmappings necessarily have well-defined tangents where they meet∂D. Using this, we obtain information about the boundaryvalues of the Jacobian transformation of f, and finally wedetermine the class of all cps-homeomorphisms of a half-planeonto itself.





Author: Julian Gevirtz

Source: https://www.hindawi.com/



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