Lipschitz continuity results for a class of obstacle problems

We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of p-type, p b 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 lead us to start a Moser iteration scheme which provides the Ll bound for the gradient. The application of a recent higher di¤erentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowdledge, this is the first result for nonautomonous functionals with standard growth conditions in the direction of the Lipschitz regularity.