Invariant cones for linear elliptic systems with gradient coupling

2021/06/10 by Dolcetta, I. Capuzzo, Rossi, L., Vitolo, A.
#35B50 #35D40 #35J47 #35J70 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.05523

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].

Related

• Stability of diffusively coupled linear systems with an invariant cone
• Weak Maximum Principle for Strongly Coupled Elliptic Differential Systems
• Existence of solutions of semilinear systems with gradient dependence\n via eigenvalue criteria
• Gradient estimates for semilinear elliptic systems and other related\n results
• Invariant convex bodies for strongly elliptic systems