Published Paper

Inserted: 25 dec 2025
Last Updated: 25 dec 2025

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Year: 2020

Abstract:

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.