TY - JOUR
T1 - SOME MAXIMUM PRINCIPLES FOR PARABOLIC MIXED LOCAL/NONLOCAL OPERATORS
AU - Dipierro, Serena
AU - Lippi, Edoardo Proietti
AU - Valdinoci, Enrico
N1 - Publisher Copyright:
Copyright 2024 American Mathematical Society.
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
KW - Mixed Gaussian and Lévy diffusion, Maximum Principles
UR - http://www.scopus.com/inward/record.url?scp=85196811850&partnerID=8YFLogxK
U2 - 10.1090/proc/16899
DO - 10.1090/proc/16899
M3 - Article
AN - SCOPUS:85196811850
SN - 0002-9939
VL - 152
SP - 3923
EP - 3939
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -