Geodesic
Weak Maximum Principle for Cooperative Systems: the Degenerate Elliptic Case
Journal of convex analysis, Tome 28 (2021) no. 2, pp. 495-508
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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.
Classification : 35J47, 35J70, 35B50, 35P30, 35D40
Mots-clés : Nonlinear elliptic systems, maximum principles, principal eigenvalues 
@article{JCA_2021_28_2_JCA_2021_28_2_a10,
     author = {I. Capuzzo Dolcetta and A. Vitolo},
     title = {Weak {Maximum} {Principle} for {Cooperative} {Systems:} the {Degenerate} {Elliptic} {Case}},
     journal = {Journal of convex analysis},
     pages = {495--508},
     year = {2021},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a10/}
}
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I. Capuzzo Dolcetta; A. Vitolo. Weak Maximum Principle for Cooperative Systems: the Degenerate Elliptic Case. Journal of convex analysis, Tome 28 (2021) no. 2, pp. 495-508. http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a10/