WEAKLY COUPLED ELLIPTIC-SYSTEMS AND POSITIVITY

In this paper we will study under which conditions the positive cone, or part of the positive cone, is preserved when solving a weakly coupl ed system of elliptic partial differential equations. Such a system wi ll be as follows: [GRAPHICS] bounded domain in R(n), with zero Dirichl et boundary condition. The operators Delta(1) will be strictly ellipti c such as the Laplacian. The system is said to preserve the positive c one if f greater than or equal to 0 implies u greater than or equal to 0. We will classify such systems. For noncooperative systems we need and show pointwise estimates for iterates of the Green function.