Some maximum principles for parabolic mixed local/nonlocal operators

Dipierro, Serena; Proietti Lippi, Edoardo; Valdinoci, Enrico

doi:10.1090/proc/16899

Some maximum principles for parabolic mixed local/nonlocal operators
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by Serena Dipierro, Edoardo Proietti Lippi and Enrico Valdinoci;

Proc. Amer. Math. Soc. 152 (2024), 3923-3939

DOI: https://doi.org/10.1090/proc/16899

Published electronically: July 31, 2024

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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, as introduced by Dipierro, Proietti Lippi, and Valdinoci [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp. 1093–1166].

Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect, which is performed by Dipierro, Proietti Lippi, and Valdinoci [J. Math. Biol. 89 (2024), Paper No. 19]. 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.

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