Invariant cones for linear elliptic systems with gradient coupling

A.Vitolo; I. Capuzzo Dolcetta; L. Rossi

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arxiv 2106.05523 v1 pith:GB4YI4IS submitted 2021-06-10 math.AP

Invariant cones for linear elliptic systems with gradient coupling

I. Capuzzo Dolcetta , L. Rossi , A.Vitolo This is my paper

classification math.AP

keywords couplingsconditionconesellipticgradientinvariantlinearorder

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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].

Invariant cones for linear elliptic systems with gradient coupling

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