We discuss counterexamples to the validity of the weak Maximum Principle for linear elliptic systems with zero and rst 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
Antonio Vitolo
2023-01-01
Abstract
We discuss counterexamples to the validity of the weak Maximum Principle for linear elliptic systems with zero and rst 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 in questo prodotto:
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