Weak Maximum Principle for Cooperative Systems: the Degenerate Elliptic Case

Italo Capuzzo Dolcetta; Antonio Vitolo

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.

Italo Capuzzo Dolcetta

Dip. di Matematica, Università La Sapienza, Rome, Italy

capuzzo@mat.uniroma1.it

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.