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

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.