A Stability Result for the $\mathrm{\infty }$-Laplace Equation

We investigate a degenerate elliptic PDE related to the $\mathrm{\infty }$-Laplace equation ${\mathrm{\Delta }}_{\mathrm{\infty }}u=0$. A stability result is derived. The $\mathrm{\Gamma }$-convergence of the corresponding functionals is investigated.