Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Antonio Vitolo

Dip. di Ingegneria, Università di Salerno, Fisciano, Italy

vitolo@unisa.it

Keywords

  • Nonlinear elliptic systems
  • maximum principles
  • principal eigenvalues

Mathematics Subject Classification

35J47, 35J70, 35B50, 35P30, 35D40

Suggested citation

I. Capuzzo Dolcetta, A. Vitolo. “Weak Maximum Principle for Cooperative Systems: the Degenerate Elliptic Case.” Journal of Convex Analysis 28 (2021), No. 2, 495–508. https://doi.org/10.68381/jca28028

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.