On a global estimate and a Stampacchia-type maximum principle for Lane-Emden systems

We establish a global boundedness result for Lane-Emden systems involving general second-order elliptic operators in divergence form and arbitrary positive exponents whose product equals one. Furthermore, we observe that, for this class of systems – and for certain operators in divergence form, including the case when both operators are the Laplacian – it is not possible to recover the classical Stampacchia maximum principle as a particular case corresponding to single equations.