  We prove Lipschitz continuity results for solutions to a class of obstacle
problems under standard growth conditions of $p$-type, $p \geq 2$. The main
novelty is the use of a linearization technique going back to [28] in order to
interpret our constrained minimizer as a solution to a nonlinear elliptic
equation, with a bounded right-hand side. This leads us to start a Moser
iteration scheme which provides the $L^\infty$ bound for the gradient. The
application of a recent higher differentiability result [24] allows us to
simplify the procedure of the identification of the Radon measure in the
linearization technique employed in [32]. To our knowledge, this is the first
result for non-autonomous functionals with standard growth conditions in the
direction of the Lipschitz regularity.
