I'm working through a book that provides the following exercise which I'm having trouble with. They cite this paper which I can't find (and even if I could, I can't read italian).

The problem:

Let $\Omega$ be a bounded open domain in $\mathbb{R}^n$ and let $E$ and $F$ be closed nonempty subsets of $\Omega$. Let $\phi \in H^1(\Omega)$ and denote by $K$ the convex set: $$K = \{v \in H^1(\Omega)\ : v \geq \phi\text{ on } E \text{ and } v \leq \phi\text{ on } F \}$$ Let $$a(u,v) = \int_{\Omega}\sum_{i=1}^nu_{x_i}v_{x_i}\,dx \quad \forall u,v \in H^1(\Omega)$$ Show that there exists a solution to the variational inequality: $$u \in K: a(u, v - u) \geq 0 \quad \forall v \in K$$