A Lewy-Stampacchia estimate for variational inequalities in the Heisenberg group

We consider an obstacle problem in the Heisenberg group framework, and we prove that the operator on the obstacle bounds pointwise the operator on the solution. More explicitly, if minimizes the functional among the functions with prescribed Dirichlet boundary condition that stay below a smooth obstacle then Moreover, we discuss how it could be possible to generalize the previous bound to a quasilinear setting once some regularity issues for the equation are satisfied.