Convergence of nonlinear elliptic operators and application to a quasi-variational inequality

This paper is composed of two parts. In the first part closedness and compactness results are given for a sequence of nonlinear elliptic operators of the form $\text{Lu  ∑}{}_{\mathrm{¦\alpha ¦?m}}\text{(?1)}{}^{\mathrm{¦\alpha ¦}}\text{D}{}^{\mathrm{\alpha }}\text{A}{}_{\mathrm{\alpha }}\text{(x, u, ▽u,…, ▽}{}^{\mathrm{m}}\text{u)}$, with monotone-type assumptions on the A_α's. These results are then used in the second part to derive existence theorems for a quasi-variational inequality related to some questions from nonlinear heat flow. This quasi-variational inequality involves a second-order operator as above and an implicit obstacle of the Signorini type on the boundary.