Serena Dipierro, Edoardo Proietti Lippi, and Enrico Valdinoci
Some maximum principles for parabolic mixed local/nonlocal operators
(63K, LateX)

ABSTRACT.  The goal of this paper is to establish new Maximum Principles for parabolic equations in the framework of mixed local/nonlocal operators. 
In particular, these results apply to the case of mixed local/nonlocal 
Neumann boundary conditions. 
Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect. 
This is particularly relevant when studying biological populations, since the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction.