STABILITY OF THE ELASTIC ENERGY IN STAR-SHAPED DOMAINS

For pure displacement boundary value problems of compressible hyperela stic materials with affine boundary values and small body forces, we s how that the energy of any smooth solution is close to the energy of t hat of the affine mapping given by the boundary condition. The energy of any minimizer is also close to that of the affine mapping provided that the minimizer exists. The main assumptions are that the reference configuration is star-shaped and the stored energy function is strong ly W-1,W-2-quasiconvex.