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Journal of Convex Analysis 28 (2021), No. 2, 495--508
Copyright Heldermann Verlag 2021

Weak Maximum Principle for Cooperative Systems: the Degenerate Elliptic Case

Italo Capuzzo Dolcetta
Dip. di Matematica, UniversitÓ La Sapienza, Rome, Italy

Antonio Vitolo
Dip. di Ingegneria, UniversitÓ di Salerno, Fisciano, Italy

We consider cooperative systems of nonlinear degenerate elliptic equations. Conditions for the validity of the weak Maximum Principle are obtained through a reduction to a single scalar equation. A suitable index related to the principal eigenvalues of the Dirichlet problems for the operators involved in the system is introduced. The positivity of this index enforces the validity of the weak Maximum Principle.

Keywords: Nonlinear elliptic systems, maximum principles, principal eigenvalues.

MSC: 35J47, 35J70, 35B50, 35P30, 35D40.

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