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.