Regularity of solutions for an integral system of Wolff type (Q624335)

The authors consider systems of fully nonlinear integral equations involving Wolff potentials: \[ \begin{aligned} u(x) &= W_{\beta, \gamma}(v^q)(x), \quad x \in \mathbb R^n,\\ v(x) &= W_{\beta, \gamma}(u^p)(x), \quad x \in \mathbb R^n;\end{aligned} \] where \[ W_{\beta, \gamma}(f)(x) = \int_0^{\infty} \left[\frac{\int_{B_t(x)} f(y)dy}{t^{n-\beta\gamma}}\right]^ {\frac{1}{\gamma-1}}\frac{dt}{t}. \] Under some conditions they prove that (1) \(u,v \in L^\infty(\mathbb R^n),\) (2) \(u,v\) are Lipschitz continuous.