The Riesz measure of \(G(\cdot )\)-superharmonic functions

In this paper, we study the relationship between Riesz measure \(\mu \) $\mu$ and \(G(\cdot )\) $G(·)$ -superharmonic functions u, which satisfies: \(\begin{aligned} -\operatorname {div} {\mathcal {A}}(x,D u)=\mu , \end{aligned}\) $$\begin{array}{c}\hfill -div\mathcal{A}(x,Du)=\mu ,\end{array}$$ in the distribution sense such that \({\mathcal {A}}(x,\xi )\cdot \xi \approx G(x,|\xi |)\) $\mathcal{A}(x,\xi )·\xi \approx G(x,|\xi |)$ and \(G(\cdot )\) $G(·)$ is \(\Phi \) $\mathrm{\Phi }$ -function.