ar X iv : m at h / 05 08 55 9 v 1 [ m at h . C A ] 2 9 A ug 2 00 5 RELAXATION THEOREMS IN NONLINEAR ELASTICITY

where detξ denotes the determinant of ξ, and (C4) W (PξQ) = W (ξ) for all ξ ∈ M and all P,Q ∈ SO(3) for N = 3, with SO(3) := {Q ∈ M : QQ = QQ = I3 and detQ = 1}, where I3 denotes the identity matrix in M 3×3 and Q is the transposed matrix of Q. (In fact, (C4) is an additional condition which is not related to (2). However, it means that W is frame-indifferent, i.e., W (Pξ) = W (ξ) for all ξ ∈ M ∗ and all P ∈ SO(3), and isotropic, i.e., W (ξQ) = W (ξ) for all ξ ∈ M ∗ and all Q ∈ SO(3), see for example [13] for more details.)