TITLE:
Uniform Hölder Bounds for Competition Systems with Strong Interaction on a Subdomain
AUTHORS:
Jiahao Ni, Shan Zhang
KEYWORDS:
Singularly Perturbation, Subdomain, Free Boundary Problem, Liouville Type Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.6,
June
7,
2023
ABSTRACT: We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.