Weakly Coupled Elliptic Systems and Positivity
نویسندگان
چکیده
In this paper we will study under which conditions the positive cone, or part of the positive cone, is preserved when solving a weakly coupled system of elliptic partial differential equations. Such a system will be as follows: −∆1 0 0 . . . 0 0 −∆k u1 .. uk = c11 · · · c1k .. .. ck1 · · · ckk u1 .. uk + f1 .. fk on a bounded domain in IR, with zero Dirichlet boundary condition. The operators ∆i will be strictly elliptic such as the Laplacian. The system is said to preserve the positive cone if f ≥ 0 implies u ≥ 0. We will classify such systems. For noncooperative systems we need and show pointwise estimates for iterates of the Green function.
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