Local and global estimates for solutions of systems involving the \(p\)-Laplacian in unbounded domains (Q2707303)

The author studies the system NEWLINE\[NEWLINE\begin{cases} -\Delta_p u=f_1(x,u,v) \quad & x\in \Omega\\ -\Delta_q v=f_2(x,u,v) \quad & x\in \Omega\\ u=v=0\quad & x\in \partial\Omega, \end{cases} \tag{1}NEWLINE\]NEWLINE where \(\Omega\subset \mathbb{R}^N\) is an exterior domain, \(p,q>1\), \(\Delta_p= \text{div} (|\nabla u|^{p-2} \nabla u)\) and \(f_1,f_2\) are given functions. The author investigates the local and global behaviour of solutions of (1). To this end the author extends some Serrin-type estimates from a simple equation to a system (1).