International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 12, Pages 739-776
doi: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 47304, IN, USA
Received 17 April 2002
Copyright © 2003 Julian Gevirtz. 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.