Harnack's inequality for cooperative weakly coupled elliptic systems

Abstract : The authors consider cooperative, uniformly elliptic systems, with bounded coefficients and coupling in the zeroth-order terms. They establish two analogs of Harnack's inequality for this class of system. A weak version is obtained under fairly general conditions, while imposing an irreducibility condition on the coupling coefficients results in a stronger version of the inequality. This irreducibility condition also is necessary for the existence of a Harnack constant for this class of systems. A Harnack inequality also is obtained for a class of superharmonic functions.