Invariant cones for linear elliptic systems with gradient coupling
Analysis of PDEs
2021-06-11 v1
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].
Cite
@article{arxiv.2106.05523,
title = {Invariant cones for linear elliptic systems with gradient coupling},
author = {I. Capuzzo Dolcetta and L. Rossi and A. Vitolo},
journal= {arXiv preprint arXiv:2106.05523},
year = {2021}
}