New results on Γ-limits of integral functionals

For Psi is an element of W-1,W-p (Omega; R-m) and g is an element of W--1,W-p (Omega;R-d), 1 < P < +infinity, we consider a sequence of integral functionals F-k(Psi,g) : W-1,W-p (Omega; R-dxn) -> [0, +infinity] of the form F-k(Psi,g) (u, v) = {integral(Omega) f(k)(x, del u, v) if u - Psi is an element of W-0(1,p) (Omega; R-m) and div upsilon = g, where the integrands f(k) satisfy growth conditions of order p, uniformly in k. We prove a Gamma-compactness result for F-k(Psi,g) with respect to the weak topology of W-1,W-P (Omega; R-m) x L-p (Omega; R-dxn) and we show that under suitable assumptions the integrand of the Gamma-limit is continuously differentiable. We also provide a result concerning the convergence of momenta for minimizers of F-k(Psi,g) (C) 2013 Elsevier Masson SAS. All rights reserved.