SynopsisLetCf, Pf, QfandRfbe respectively the convex, polyconvex, quasi-convex and rank-one-convex envelopes of a given functionf. If fp: RNxM→R andfq(ξ) behaves as |ξ|qat infinityq∈ (1, ∞), we show that. This is the case for (Pfp)pprovided thatq≠1,…, min (N, M), otherwise. In the last part of this work, we show thatf(ξ) = g(|ξ|) does not imply in generalPf = Qf.
Linear convergence in the approximation of rank-one convex envelopes