Nonlinear Calder\'on-Zygmund inequalities for maps

Being motivated by the problem of deducing $L^p$-bounds on the second fundamental form of an isometric immersion from $L^p$-bounds on its mean curvature vector field, we prove a (nonlinear) Calder'on-Zygmund inequality for maps between complete (possibly noncompact) Riemannian manifolds.