2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125927In this paper, we consider the analogous of the obtacle problem in $H_0^1(Ω)$, on the space $W^{1,p}_0(Ω)$. We prove an existence and uniqueness of the result. In a second time, we define the optimal control problem associated. The results, here enclosed, generalize the one obtained by D.R. Adams, S. LenhardAnalysis of PDEs49xx, 34Kxx, 65K10text