Extending the Knops-Stuart-Taheri technique to $C^{1}$ weak local minimizers in nonlinear elasticity

Abstract

We prove that any C 1 weak local minimizer of a certain class of elastic stored-energy functionals I(u) = ∫ Ω f(∇u) dx subject to a linear boundary displacement u 0 (x) = ξx on a star-shaped domain Ω with C 1 boundary is necessarily affine provided f is strictly quasiconvex at ξ. 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 +∞ in an essential way.