Published Paper

Inserted: 25 dec 2025
Last Updated: 31 dec 2025

Journal: ESAIM Control Optim. Calc. Var.
Year: 2020

Abstract:

In this paper, we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $\min\left\{\int_{\Omega} F(x, Dz) : z \in \mathcal{K}_\psi (\Omega)\right\}.$ Here $\mathcal{K}_\psi(\Omega)$ is set of admissible functions $z \in W^{1,p}(\Omega)$ such that $z \ge \psi$ a.e. in $\Omega$, $\psi$ being the obstacle and $\Omega$ being an open bounded set of $\mathbb{R}^n$, $n \ge 2$. The main novelty here is that we are assuming $ F(x, Dz)$ satisfying $(p,q)$-growth conditions {and less restrictive assumptions on the obstacle with respect to the existing regularity results}.