Crooks, E.C.M. and Dancer, E.N. (2011) Competition Systems with Strong Interaction on a Subdomain. Topological Methods in Nonlinear Analysis, 37, 37-53.

has been cited by the following article:

• 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.