A strong convergence of the weak gradient to A-harmonic type operators with L1 data

We prove u(k) -> u strongly in W-loc(1,q)(Omega) with 1 <= q <= p by Lipschitz truncation argument if u is an element of W-1,W-p(Omega) is a weak solution of A-harmonic type equations -divA(x, Du) = f (x) with f is an element of L-1 (Omega), and u(k) is a sequence of their weak solutions with u(k) -> u weakly in W-1,W-p(Omega) and f(k) -> f weakly in L-1(Omega). As an application, we obtain a compactness property for p-harmonic maps defined from L-infinity-metric Riemannian manifold. (C) 2015 Elsevier Inc. All rights reserved.