  0.  $\Omega$ is an open, bounded and $G$-invariant subset of an orthogonal $G$-representation ${\mathbb{R}}^n$, with a smooth boundary,  0.  $F\in C^0({\mathbb{R}}^0,{\mathbb{R}})$,  0.  $|\nabla^0 F(y)|\leq a +b|y|^q$, where $a,\ b\in{\mathbb{R}},\ q<\frac{0}{n-0}$ for $n\geq 0$ and $q<\infty$ for $n=0$.  