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arXiv · 2106.05523

Invariant cones for linear elliptic systems with gradient coupling

I. Capuzzo Dolcetta·L. Rossi·A. Vitolo
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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 [21].

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I. Capuzzo Dolcetta, L. Rossi, A. Vitolo. 2021-06-10. Invariant cones for linear elliptic systems with gradient coupling. https://arxiv.org/abs/2106.05523

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