A Diagonal Hyperbolic System for Mappings with Prescribed Principal Strains

We derive a diagonal hyperbolic system of n(n + 1 )(n + 2)/2 equations satisfied by the component functions of an n-dimensional mapping with given distinct principal strains together with certain combinations of their first and second order derivatives. This permits us to treat, in an elementary manner and under weak regularity assumptions on the initial data, the natural initial value problem for such mappings studied previously by D. DeTurck and D. Yang (Duke Math. J.51, 1984, 243-260) and throws light on the mechanism behind the formation of singularities.