EXTENDING THE KNOPS-STUART-TAHERI TECHNIQUE TO C1 WEAK LOCAL MINIMIZERS IN NONLINEAR ELASTICITY

We prove that any C-1 weak local minimizer of a certain class of elastic stored-energy functionals I(u) = integral(Omega) = f (del u) dx subject to a linear boundary displacement u(0)(x) = xi(x) on a star-shaped domain Omega with C-1 boundary is necessarily affine provided f is strictly quasiconvex at xi. This is done without assuming that the local minimizer satisfies the Euler-Lagrange equations, and therefore extends in a certain sense the results of Knops and Stuart, and those of Taheri, to a class of functionals whose integrands take the value +infinity in an essential way.