  We start presenting an $L^{\infty}$-gradient bound for solutions to
non-homogeneous $p$-Laplacean type systems and equations, via suitable
non-linear potentials of the right hand side. Such a bound implies a Lorentz
space characterization of Lipschitz regularity of solutions which surprisingly
turns out to be independent of $p$, and that reveals to be the same classical
one for the standard Laplacean operator. In turn, the a priori estimates
derived imply the existence of locally Lipschitz regular solutions to certain
degenerate systems with critical growth of the type arising when considering
geometric analysis problems, as recently emphasized by Rivi\`ere

Analysis of PDEs