We discuss counterexamples to the validity of the weak Maximum Principle for linear elliptic systems with zero and first order couplings and prove, through a suitable reduction to a nonlinear scalar equation, a quite general result showing that some algebraic condition on the structure of gradient couplings and a cooperativity condition on the matrix of zero order couplings guarantee the existence of invariant cones in the sense of Weinberger [22].
Invariant cones for linear elliptic systems with gradient coupling / Capuzzo Dolcetta, I.; Rossi, Luca; Vitolo, Antonio. - In: PURE AND APPLIED FUNCTIONAL ANALYSIS. - ISSN 2189-3756. - 8:1(2023), pp. 117-132.
Invariant cones for linear elliptic systems with gradient coupling
I. Capuzzo Dolcetta;Luca Rossi;
2023
Abstract
We discuss counterexamples to the validity of the weak Maximum Principle for linear elliptic systems with zero and first order couplings and prove, through a suitable reduction to a nonlinear scalar equation, a quite general result showing that some algebraic condition on the structure of gradient couplings and a cooperativity condition on the matrix of zero order couplings guarantee the existence of invariant cones in the sense of Weinberger [22].| File | Dimensione | Formato | |
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